Digital Finance:  Cash, Credit, and Investment Instruments in a Unified Framework (BitMint)

ABSTRACT

Presenting a framework for digital finance based on the notion of a unified digital expression to value and identity which carries this value—advancing beyond the standard form of digital finance where value (a number) is expressed without any coin, or bill identity. The solution is based on ordered financial bits (fbits) which may be comprised of ingredient fbits, or of elemental fbits which are qbits—real or simulated. As such this solution (BitMint) is ready for quantum computing when it materializes commercially. A BitMinted entity carries its terms of exchange, and redemption; it may carry its transactional history, and apply equally to cash, credit and investment instruments. It allows full operational flexibility to its controllers who mint and redeem it. The BitMinted entity, BitMint “coin”, or simply “coin” will keep transacting even if the Internet is slow, or jammed. The coin may be cut to any small denomination desired, or lumped to any large sum of interest. It spans from international payments, to Internet-of-Things value exchange. The BitMint coin will flip at will from transactional privacy to transactional transparency, and back. Designed as a national currency framework, the BitMint coin lends itself to fair, efficient and transparent taxation. BitMint is the mathematically optimized solution to the objective of combining identity and value into a non-separable value carrier (coin).

Our fast technological pace poses a risk of obsolescence to any digitalmoney design wedded to the present. Req #1: Digital Money Today ShouldAnticipate Quantum Computing Tomorrow. And until then we should build adigital financial framework based on bits to be transformed into qbits.

We Must Design Digital Money as a Comprehensive Platform for all thingsfinancial Req #2: Cash, Credit, and All Financial Instruments Should fitinto the Same Format. Much as the chemical elements in the PeriodicTable fit into the same atomic framework, allowing for chemical bonds—soshould financial elements interact

The newly designed digital money should incorporate a rich toolbox forcentral banks to intervene and take steps to insure economic stability.Req #3: Digital Money Should Enable its Controllers to use Money to BestServe Society. Inflation, deflation, employment, should be manageable.

Unstable Money flow leads to unstable society. Society should notoutsource its Ultimate responsibility to Control Monetary dynamics Req#4: Algorithms and AI Should Support, not Replace Central Banks.Algorithms Fail Miserably when confronted with a situation notenvisioned by their designer.

The Internet makes payment fast and convenient, but payment can't bedependent on the Internet never failing, never slow. Req #5: DigitalMoney Should be Transactable Even When the Internet is Jammed, or BrokenDown. Money must flow during emergencies, war, hostilities and naturaldisasters.

One digital system should handle large, very large, medium, small, andvery small transactions—fast and secure (frictionless). From theInternet of Things to International Banking. Req #6: Digital MoneyShould be Payable at Any Desired Resolution: Micro even Nano Payments toNational Bills. Applicable to money in motion and to money at rest.

Public Serving Banking Databases will Eventually be Compromised.Ultimate protection of the Mintage is mandatory. Req #7: The UnderlyingFoundation of a National Digital Money System Must Be a Well-GuardedPhysical Embodiment. Implicit data captured in solid chemistry can't behacked.

Privacy of Transactions is a critical aspect of freedom and demanded bythe Public. Same Privacy is abused by financial fraud, and must becontrollable by government. Req #8: Digital Money Must be Flip-Readyfrom Transactional Privacy to Transactional Transparency Digital Coinsshould be passed around cash-like, but maintain a complete record ofchain of custody when warranted.

Taxation and Funding of Government must be evasion-resistant Req #9:National Digital Money Must Lead to Fair and Efficient Taxation.Taxation should not be an after-thought when designing a new longlasting digital money framework. Efficient and fair taxation should be aprime design feature

The mathematics underlying Crypto Currencies has no mathematical Proofof Efficacy Req #10: We Must Design Digital Money So That It Is NotVulnerable To A Mathematician Smarter Than Its Designer. The Effect of abreach of a Bitcoin-like Crypto Math is Catastrophic. All the wealthdisappears overnight.

How This Invention—The BitMint (Inclusive) Coin—Meets TheseRequirements: Req #1: Digital Money Today Should Anticipate QuantumComputing Tomorrow The BitMint (inclusive) coin anticipates the futuretechnology where a string of qbits will be maintained in a stablecondition. These qbits then will carry the value of the BitMint(inclusive) coin via the various fbits. Until such time, qbits aresimulated by quantum-randomness sources that are activated just when thecoin is minted. Time tagging the moment of being aware of the bitidentities of a coin, is a way to prove the instant of ownership, so nopost transaction settlement is necessary.

Req #2: Cash, Credit, and All Financial Instruments Should fit into theSame Format. The BitMint (inclusive) coin is designed as a framework forcash, credit, and resource allocation. Any thing financial may berepresented through configured fbits, associated with a transactionalterms.

Req #3: Digital Money Should Enable its Controllers to use Money to BestServe Society. Unlike cryptocurrencies which are ruled by a package ofpre-set rules, the BitMint (inclusive) coin is centrally minted and themint and redemption controllers are empowered to introduce any ad-hoc,emergency, or unplanned actions to meet any unexpected surprise.

Req #4: Algorithms and AI Should Support, not Replace Central Banks.While the routine minting and redemption of coins is algorithmicallydone and procedurally determined, the mint owners have the power tointervene, stop, modify any algorithmic mint action.

Req #5: Digital Money Should be Transactable Even When the Internet isJammed, or Broken Down. BitMint (inclusive) coin are transacted bypassing bit information from payer to payee. This can be done withbattery-operated devices while the Internet is down. The bit-wise coininformation may be even traded as a printout of QR code or bar code.

Req #6: Digital Money Should be Payable at Any Desired Resolution: Microeven Nano Payments to National Bills. The mint may express any smallamount of money with fbits identified by as many bits as desired, andvice versa, any large sum may be fbit expressed in a nominal way.

Req #7: The Underlying Foundation of a National Digital Money SystemMust Be a Well-Guarded Physical Embodiment. BitMint (inclusive) coin maybe expressed through the ‘rock of randomness’ technology and ρcoins.

Req #8: Digital Money Must be Flip-Ready from Transactional Privacy toTransactional Transparency. The mint may dictate terms of redemption.There may be full disclosure of custodial history of each coin, or itmay be blind to what happens with a coin from minting to redemption. (oranything in between).

Req #9: National Digital Money Must Lead to Fair and Efficient Taxation.BitMint (inclusive) coin is readily taxed through forced coin splitting.

Req #10: We Must Design Digital Money So That It Is Not Vulnerable To AMathematician Smarter Than Its Designer. BitMint (inclusive) coin isbased on quantum randomness not on crackable math. BitMint (inclusive)coins are not vulnerable to powerful computers beyond the computingcapacity of the mint.

DETAILED DESCRIPTION OF THE INVENTION

The core capability of the BitMint system is to generate a digitalequivalent for money. The essential feature of the digitized entity isthat it represents a well-defined monetary value fused with a uniqueidentity that distinguishes this representation of value from any otherrepresentation of the same value. Much as a banknote comes with a serialnumber that distinguishes it from any other bill of the samedenomination.

The unique and most powerful feature of BitMint money is its method fordigitizing any fiat currency or any commodity. The BitMint moneyrepresentation insures that every expression of value will be borne by aunique entity. This is a subtle and profound distinction over thetraditional way that money is represented in a computerized environment.Today about 90% of all the money in the world, is never reduced to aphysical coin or to a paper bill. It is stored and transacted ascomputer entries. Money, today, by and large, is a number stored in acomputer address. That number increases to show more money, and it isdecreased to show less money. Hence payment is never a direct transferof ‘something’ rather it being a negotiated adjustment of credit.

The essential characteristics of “legacy digital money” (the money thebank currently uses) is the loss of money identity. This loss wascorrected by crypto currencies like bitcoin, but at an exorbitant price:indelible complexity.

BitMint achieves this combination of identity+simplicity by a simpleprinciple: not allowing the identity of bits to express monetary value.Identity of bits is reserved to express the identity of the BitMintdigital coin. This way the resultant BitMint coin may be expressed viaqbits, or simulated qbits, in as much as the value of the coin may bethe same regardless of the identity of bits. This fact is thefundamental distinction of BitMint from other digital money solutions.In other solutions the bit identities plays a role in determining thevalue of the coin. Not so in BitMint. BitMint expresses monetary valuethrough a mathematical construct called the BitMint digital coin. Themonetary value of the BitMint digital coin, (BitMint coin, or coin forshort) is expressed through a string of bits where the identity of thebits is not a factor in the determination of the value of the coin. Inits basic form Monetary value is determined by bit position—by the placeof each bit in the string of bits knows as the “payload”—the money bits.Counting from left to right, bit in position i is associated with avalue function v(i), which runs from i={first bits in the coinstring−the payload} to i={last bit in the coin string}.

Monetary value is expressed via the BitMint-Valuation Function (BMV),which assigns a monetary value V to coin x as follows:

V _(x) =Σv(i) for i=1 to i=|x|

Where i is a running count of the BitMint coin payload bits startingfrom the first bit on the left, and ending with the last bit on theright, and v(i) is the BitMint-bit value function. Notice that thisformula does not specify the identity of the bit. Therefore the bit caneventfully be a qbit, or a simulated qbit. We distinguish:

-   -   v(i)>0 indicates that bit i (regardless of its identity) has a        cash value of |v(i)|$.    -   v(i)=0 indicates that bit i (regardless of its identity) has no        cash value of |v(i)|=0 $.    -   v(i)<0 indicates that bit i (regardless of its identity) has a        negative cash value of |v(i)|$.

Positive cash value is spendable cash, negative cash value is debit,obligation to pay. Zero cash value implies in essence a “place holder”for money. In general each BitMint bit (regardless of its identity) canbe associated with any number of valuation functions which may, or maynot be cross-exchanged. The bit integral value function of a BitMintcoin, V(i) is defined as: V(i)=Σv(j) for j=1 to j=i. And may takevarious forms.

This representation of monetary values is a generalization of money inas much as it encompasses in one unified expression the management ofpositive value (cash and any financial instrument of credit, and riskallocation), the management of debt and obligation, and the managementof virtual money (entities that behave like money but are not). Everyfinancial entity of any kind can fit into the same financial rails, theway the train railways are fit for passenger trains and cargo trains.This unified railway is handled with maximum speed, ease andconvenience, because it is bit-wise. It is handled with pin-pointedfocus on intended use—with no diversion or misuse—owing to its format ofunbreakable combination of money-value and money-identity. And all thatunder the unassailable protection of quantum-physics grade randomness,and with full readiness for commercial qbits. It's the rails to drivethe financial trains to the 21st century. In its advanced form BitMintcoins may carry several valuation functions and thereby express complexfinancial arrangements. BitMint coins may eventually split such thateach split will assume a different part of the valuation function of thepre-split coin.

To represent a monetary value of x$ in the BitMint platform, (basicmode) one will put together a bit string S comprising s bits, where eachof these bits is assigned a value v(i) for i=1,2, . . . s, such that:x=Σv(i) for i=1 to i=s It is noteworthy that this value formula does nottake into account the identity of bits in S.

Illustration: One would represent the value of x=16$ using 7 bits suchthat the value of these bits given below:

bit # value ($) 1 3 2 6 3 2 4 5

The value of these bits is: x=Σv(i)=(3+6+2+5)=16

Please note that this value could be represented by any one of thepossible 16 strings: 0000, 0001, 0010, 0100, 1000 0011, 0110, 1100 0101,1010 1001 0111, 1110 1101, 1011, 1111

This implies that the valuation function that assigns a monetary valueto a string of bits is not pointing to the specific string of the coin.Given the monetary value (e.g. 16$ per 4 bits) one faces a 16 foldequivocation as to the identity of the string that was used to generatethis sum of money. Below we expand on the above, discussing (i) coinsplitting, (ii) bit identities, (iii) financial bits (fbits), (iv) coinstructure

BitMint Coin Splitting

This (basic mode) BitMint representation of monetary value as a BitMintdigital coin lends itself to coin-splitting. A BitMint coin of valuex=V_(x) $, is written as a string X comprised of s=|X| bits, such that:x=Σv(i) . . . for i=1 to i=s

Let T be a substring of X (T∈X), such that T starts with bit t_(a) andstretches up to bit t_(b) in X. We associate this substring with amonetary value V(T) as follows: V(T)=Σv(i) . . . for i=t_(a) to t_(b)

Clearly V(T)≤x. The string T will be defined as a split-coin of x, andwill in turn split coin x to one, two, or three splits. We can write:x=V(T′)+V(T)+V(T″) where T′ is the substring of x that stretches frombit 1 to bit (t_(a)−1), and T″ is the substring of x that stretches from(t_(b)+1) to s. If t_(a)=1 then T′=‘NULL’ (the null string), becauset_(a)−1 does not exist, and if t_(b)=s then T″=‘NULL’ because t_(b)+1does not exist.

Illustration: let a BitMint coin be expressed via a bit string X,comprised of 10 bits where v(i)=i$. The value of the coin is:V(X)=1+2+3+4+5+6+7+8+9+10=55

We can define a substring T on X with t_(a)=3 and t_(b)=7. Its valuewill be: V(T)=3+4+5+6+7=25

So X will be divided to T′ stretching from bit 1 to bit t_(a)−1=2, T,and T″ stretches from t_(b)+1=8 to 10. So T′=1+2=3, and T″=8+9+10=27.And indeed V(X)=V(T′)+V(T)+V(T″)=3+25+27=55

Each split-coin can be regarded as a bona fide coin, which means that ittoo can be split. Splitting hence is recursive. Eventually a BitMintcoin x may be split to n split-coins: X=T₁∥T₂∥ . . . T_(n) Wheresubstring T_(i) stretches from t_(ia) to t_(ib), for i=1,2, . . . n,where: t_(ib)+1=t_((j+1)a) so that: V(X)=ΣV(T_(i)) i=1,2, . . . n

Coin Identity

Since the identities of the BitMint bit-wise coin are not playing anyrole in determining the value of the coin, they can be determined toserve other purpose. Digital coins serve as a very attractive target tofraudsters. The lack of physicality opens opportunities for theft waybeyond what is possible with physical coins. Any ambition to replacephysical money as a robust money system will have to wrestle with thechallenge of integrity and security.

Legacy money faces this challenge through an elaborate set of fences ofchecks and balances. Nominal crypto currencies meet this challenge withalgorithmic intractability. The critique of this strategies is describedin the book “Tethered Money” (Elsevier, 2015). BitMint meets the samechallenge by using the freedom to set the identities of the coin bits.Any algorithmic method to set up those identities will inherently besubject to successful cryptanalysis, compromise. Therefore BitMintdetermines the identities of the value bits of the BitMint coin withoutuse of deterministic tools. The identities of the BitMint coins is setup through randomness. This indeterminism is the essence of qbits, whichwill be used by BitMint as soon as the technology is sufficientlywidespread. Until then BitMint will simulate the indeterminism of bitidentity by leaving it undetermined until the very moment of minting thecoin, and at that moment a quantum-grade source of randomness will setup the bit identity.

Any digital coin where the payee may apply an algorithm to the paymentto decide its bona fide, will be unsustainable because the determiningalgorithm will have to be made public, and hence allow an attacker tobrute-force check fake money again and again until he finds a fake moneystring that passes the determining algorithm. For decades researcherswere developing such a smart algorithms before realizing that it ishopeless. It is time to turn to randomness.

The mature BitMint coin will be in a quantum state (full quantum mode).This state will be used to detect man-in-the-middle attacks, and tocarry tethering information. Qbits technology is not yet sufficientlyadvanced to be incorporated in the BitMint payment platform, but theBitMint designers are looking forward to the day when quantum computingwill be in play, and this framework is designed to enable a seamlessadaptation of the new technology.

In the meanwhile we use one step below qbits—we use qbits until weactivate a payment activity, at which point the qbits collapse toregular bits (partial quantum mode). This strategy prevents any would beattacker from compromising the bits ahead of their time of use. Andsince the collapse of bits is patternless, the collapsed qbits challengetheir attacker with maximum probability defense. This probabilitydefense is exponentially proportional to the number of bits involved.Mindful of that, BitMint was designed with an interplay between theBitMint valuation function equivocation and the bit count. This allowsthe mint to gauge its probability defense to its preference by adjustingthe BitMint valuation function to employ enough bits to provide asufficiently robust probability defense.

BitMint may be implemented in low-risk environments where the monetaryvalue of the transmitted coins is way too small to attract a seriouscryptanalysis effort. Such mints may be using upgraded algorithmicrandomness. This is a solution that is based on pseudo-randomness thatis processed through an upgrading filter. The randomness filter discardssubsections of bits which are not random enough. Enhanced algorithmicrandomness is easier, cheaper and operationally more reliable thantrue-randomness sources. (Detailed in US Patent Application #15898876).

Financial Bits

We introduce the notion of ‘financial bits’ with an operational mindset.For a more abstract and comprehensive view please consult the sectionentitled: “BitMint (inclusive) Construction Scheme”.

Financial bits (fbits) in their basic form are value bits in a BitMintcoin. They are identified by their position (i) in the BitMint moneystring, and they can be associated with one or more valuation functionv_(i)(i), v₂(i), . . . . Regular bits in a BitMint value string are bitsthat qualify as financial bits (fbits). Albeit, this notion of afinancial bit can be expanded to be assigned to a string off consecutivebits, to be regarded as a single financial bit: {f regular bits}→{1fbit}

Illustration: Let A be a 12 bits string: A=‘1 0 0 0 1 0 1 1 0 0 1 0’ wecan define it as comprised of 4 financial bits, where each financial bitwill be comprised of 3 regular (nominal) bits. A=B₁−B₂−B₃−B₄, whereB₁=‘1 0 0’, B₂=‘0 1 0’, B₃=‘1 1 0’, B₄=‘010’. Each financial bit will beassigned a valuation function, say v(i)=10+i. We can write then:

v(B₁)=11, v(B₂)=12, v(B₃)=13, v(B₄)=14, and henceV(A)=Σv(i)=11+12+13+14=50.

The financial bits are the smallest unit of financial reference. It ismeaningless to ask, what is the value of a nominal bit in A, or ask thesame with respect to any group of bits other than a group off nominalbits that is properly packed into a financial bit. We reserve the symbolφ for a financial bit. Accordingly, a BitMint coin will be expressed viaa payload (value bits) written as a string of financial bits:

=φ₁ φ₂, . . . φ_(s) where s is the count of financial bits in the coin,marked as

or as “<0|1>”.

Expanding nominal bits to financial bits comprised off nominal bitsoffers new operational capabilities. They are of two kind: identity andsecurity as one kind; data and attributes as a another kind. In generalthe f bits of a financial bit will be divided to f_(i) identity bits,and f_(d) data bits: f=f_(i)+f_(d).

The Identity Bits within a Financial Bit: A financial abuser would facea 50% of correct guess of the identity of a single nominal bit. Howeverwith respect to a financial bit comprised of f_(i) nominal bitsdedicated to identity, the chance of correct guess drops to 2^(−f) _(i).And since the BitMint coin designer has full control over the value off_(i), she also has full control over the probability defense againstthe chance to correctly guess the identity of a financial bit. We mustbear in mind that the operation of BitMint is based on the idea thatrightful holders of a BitMint coin know the identity of the financialbits, while others know it not. We designate the f₁ identity bits as φ{.. . }

The Data Bits within a Financial Bit: These bits will indicate data in anominal way. The f_(d) data bits may carry 2^(f) _(d) distinct messages,or data items. This data may be of any kind. Some utility options are:(i) counters, (ii) pointers, (iii) valuation parameters.

fbit counters: Some f_(dc)≤f_(d) bits may be assigned to count somesteps from an initial zero count position to a maximum of 2^(f) _(dc)counts before it counts from the starting point again. So for exampleevery time the coin changes hands the counter increments. The value ofthe counter could be compared to meta data that tracks chain of custodyto flash out inconsistencies.

fbit pointers: Some f_(dp)≤f_(d) data bits may be allocated to point tothe position of the fbit in the BitMint coin, or to the position of thenext or precedent fbits in the coin. One pointer will state whether thisbit is the first in the coin, the last in the coin, or somewhere inside.Another fbit bit will carry a flag that will also be carried by the nextfbit despite its location elsewhere in the system and thereby the fbitswill be able to handle physical separation of a coin.

valuation parameters: Some f_(dv)≤f_(d) bits may be used to specifyparameters of the fbit valuation function. Let F_(d) be the data carriedby the f_(d) data bits. The respective valuation function for thefinancial bit may be defined as v(i,F_(d)), where i is the count of thisfbit in the BitMint coin. The ratio f_(i)/f is regarded as the “DataIdentity Index” (DII=f_(i)/f) of the BitMint coin. Clearly if DII=0, thedata identity index is zero, or say, the data is expressed in a nominalway, no bits are allocated to express identity. From a securitystandpoint DII=0 means that the data is ‘naked’ and its protection isgiven to external fences. On the other hand for DII=1, the data isexpressed with maximum identity indication, but there is no room fordata bits (f_(d)=0). The case of DII=1 is the case of maximum inherentsecurity. In general every extra identity bit double the inherentsecurity of the data.

Illustration: Let a BitMint coin be constructed from 4 financial bits,of size f=16 bits, of which f_(i)=13 bits and f_(d)=3. bits. The databits (f_(d)) will be comprised of one pointer bit (f_(dp)=1), nocounters (f_(dc)=0) and 2 value bits (f_(dv)=2). The chance for anattacker to guess this fbit right is: 2⁻¹³=0.00012. The pointer be willbe set to be F_(dp)=1 for every fbit that is either the first or thelast fbit in a coin, and set to be F_(dp)=0 otherwise. F_(d) representsthe data expressed in the f_(d) bits. The two value bits will beinterpreted in straight binary value F_(dv)={0,1,2,3}, and the valuefunction for each fbit will be: V(i)=1+2^(F) _(dv) ⁺¹ for i=1,2,3,4

The fbit is constructed in the following sequence: f_(i)−f_(d), and thedata bits are constructed as f_(dp)−f_(dv). Accordingly, the BitMintcoin will be set as follows:

{BitMint coin}=1001 0110 1101 0 1 11 0011 0111 0111 0 0 10 0011 11100101 1 0 10 0100 0101 1111 0 1 00 And interpreted as follows:

Id p v 1001 0110 1101 0 1 11 0011 0111 0111 0 0 10 0011 1110 0101 1 0 100100 0101 1111 0 1 00

The value of this BitMint coin will be: 17+9+9+3=38$

Binary Value Representation

The most convenient way to represent values in computing devices isthrough the binary series. Accordingly a good BitMint coin structuredesign will be with a number of value bits f_(dv)=n, combined with aBitMint valuation function v(i)=2^(m) for m=0,1, . . . (n−1).

The BitMint coin will have any value N$ will be expressed through astring comprised of s₀ fbits where: s₀=Σs_(i) . . . for i=1 to 2^(n)where {s}_(n) is a solution to the following binary value equation, forN, the desired value of the coin N=Σs_(i)*2^(m) _(i) . . . for i=1 toi=2^(n) where 0≤m_(i)<2^(n)

For any N and n there are very many solutions for {m}_(n) and {s}_(n).Note that:

2^(x)+2^(x)+ . . . +2^(x)=2^((y−x))*2^(x)=2^(y)

Illustration: Our goal is to mint a BitMint coin to carry the value of1000$. Expressing in binary:

N=1000=2⁹+2⁸+2⁷+2⁶+2⁵+2³

For f_(dv)=4, one can mint the value N with 6 fbits:

N _(BitMint)=[{ . . . }F _(dv)=9][{ . . . }F _(dv)=8][{ . . . }F_(dv)=7][{ . . . }F _(dv)=6][{ . . . }F _(dv)=5][{ . . . }F _(dv)=3]

where “[ ]” denotes an fbit and { . . . } denotes the identity bits ineach fbit. Or, say:

{s} ₂ ⁴={0,0,0,0,0,0,1,1,1,1,1,0,1,0,0}

In the case where the architecture of the minted coins prescribesf_(dv)=3 but the sequence ‘111’ is reserved for some other signal, thenN will have to be expressed with power indices: 0,1,2,3,4,5,6. We writetherefore:

2⁷=2⁶+2⁶ 2⁸=2⁶+2⁶+2⁶+2⁶ 2 ⁹=2⁶+2⁶+2⁶+2⁶+2⁶+2⁶+2⁶+2⁶

We therefore will need (1+2+4+8)=15 fbits with F_(dv)=6, plus fbit withF_(dv)=5, and another fbit with F_(cv)=3 And we can write:{s}₆={15,1,0,1,0,0}

BitMint Coin Structure

The BitMint coin is comprised of the “payload”, these are the BitMintvalue bits (or rather BitMint fbits), and all the other bits, the “metacoin” or “meta data” that accompanies the payload so that the coin mayfit into the trading platform. The meta-coin is comprised of: headerIdentification, Tether, Accounting, Security, trailer.

Except identification, all other meta coin fields are optional. Theheader and the trailer are needed when the BitMint coin is mingled withother data. These data fields bound the coin from what comes before andwhat comes after. If a coin is split then the first part is back stampedwith a split-one tag, and the second part is headed with a split-twotag.

Header, Trailer, and Split

The header and the trailer are designed as boundary for the coin string.They assure their observer that no additional coin information ismissing. Given a stream of coins, the way to separate them is byspotting these tags. This holds in the general case when the size of thecoin varies. There exists a design option under which the size of allcoins will be the same. It happens when using null valuation functionson fbits, which are placed so as to insure that the given coin fits in astandard size. In that case, the need for a header and trailer is lesspronounced. Note: coin integrity will also be assured withhash-signatures.

The splits tags are used to handle a coin stream which is truncatedaccording to other considerations and may result in splitting a coininto two parts. The split-1 and split-2 tags are designed to keep trackof the splits.

Identification

The identification section is comprised of:

Mint Identification: This identification is of special importance in anenvironment where more than one mint operates.

Coin Identification: This is a unique coin identifier. There should beonly one tuple of Mint-id—Coin-id. The power of BitMint is in theinseparability of the value and the identity of the coin. Hence the idis as important as the value. Coins will retain their unique id evenafter been redeemed and out of play. The coin is is passed on to all thesplit-off coins.

Status: A tag to indicate the status of the coin. Options: (i) ready(unborn), (ii) live and well, (iii) live and sick, (iv) dead, notburied, (v) dead and buried. Status dynamics is reported in theaccounting section,.

Split Identification: Data to specify the subsection of the BitMintcoin. Would normally identify the starting fbit and the ending fbit, oreither one of them and the bit length of the payload section thatcomprises this split.

Time Stamp: Record of time of Minting, and Time Stamp of redeeming. Timestamp should be in a resolution of 1 second or even shorter, because thedata may be used in various security protocols.

Coin Status: A tag to indicate the status of the coin. Options:

(i) ready (unborn), A minted coin that has not yet been activated (sentto a trader) will be in this status option. It is desirable that thisstatus option will be short lived. The intent is to mint BitMinton-demand, to reduce chance of pre-use compromise.

(ii) live and well, This is the nominal status for a circulating coin.This is the only status of a coin which makes it redemption-eligible.

(iii) live and sick, This status indicates some problems with the coin,perhaps data corruption, some security alert, or due flagging by theauthorities.

(iv) dead, not buried, A dead coin is a coin that was redeemed, where‘not buried’ indicates that it is still in a ‘challenge option’ periodwhere it is possible for a challenger to contest the payment.

(v) dead and buried, This status option reflects the fact that the coinwas redeemed and out of circulation, with no option to challenge orresurrect.

Status dynamics is reported in the accounting section.

Tether

The tether section provides information about tethering the coin tospecified redemption conditions. We identify:

Redeemer Terms, Coin Terms, History Terms, Blockchain Terms, InsuranceTerms, Owner Certificate.

The redeemer terms identify the redeemer as meeting specified terms asto who may redeem the BitMint coin. The coin terms specify terms to bemet before this coin can be redeemed. History terms refers to the chainof custody over the coin as logged in the accounting section of thecoin. The coin is redeemed only if its custodian history, or other termshave been met. Blockchain terms refers to redemption terms validated byblockchain technology. Insurance terms refer to a situation where athird party takes over the inspection of the transaction, and thenissues a ‘good to redeem’ certificate. If this redemption relates to anyfraud, the insurer indemnifies BitMint. An owner certificate is a datasignal issued by the owner of a BitMint coin to a redeemer, such thatupon presentation of the certificate the money is released without anyfurther conditions.

In general a BitMint coin will be redeemed only if all the requiredterms are met. The BitMint mint may also adopt a delay policy,accordingly under some conditions a redeemed coin is actually redeemedafter some time delay, to account for a fraud situation where the victimtries to redeem the same coin a short while later. The coin will carrythe tether data, which in turn will be processed by tether software runby the mint.

The tether field will always designate a master—one who could modify thetethering terms. This is important because coins may be stuck intonever-redemption status, and would remain unredeemed indefinitely. Themaster is usually the trader who ordered the tethering.

Redeemer Terms

The redeemer terms may be identified as follows:

Any Redeemer: The case of no tethering, no restrictions. The first topresent the coin for redemption will get the money. This no-tetheroption may still require the redeemer to specify his or her identity toreceive the redeemed money.

Registered Redeemer: This is the case where traders are expected toregister with the mint, and identify themselves when they redeem a coin.

Community Redeemer: Redemption may be restricted to redeemers who belongto a specified group. Redeemers then need not to identify themselvesindividually only as members of the group.

Id Verified Redeemer: This is the case where a redeemer must submitpersonal credentials to prove his or her identity. There exists a largevariety for this category, from a replaceable personal identificationnumber, to a public/private key scheme, bio-identifiers etc.

Coin Terms

Any logical conditions in any logical combination may be set as cointerms. Given a set of n terms, then they may be combined in severaloptimal ways to lead to a go/no-go redemption decision. It can be aregular “AND” over all the terms, meaning all terms have to be met forthe coin to be redeemed. It may be an “OR” box where either one of theterms must be fulfilled in order to redeem the coin. Or it may be somecombination of AND and OR. The combination of the terms may beconfigured as a “partial AND” where some subset of the terms must befulfilled for redemption to occur.

History Terms

If the BitMint coin includes chain of custody information then the mintwill check that the coin did not pass through the wrong hands. Somecoins may be restricted for use within a closed circle. This also can bechecked by the redemption decision algorithm. .

Blockchain Terms

A BitMint coin may be traded on a blockchain protocol and as such theredeemer will have the public ledger to prove his ownership. Theblockchain protocol may also prove the fulfillment of certain redemptionconditions. In that case the BitMint redemption algorithm will inspectthe public ledger and decide on redemption.

BitMint coins may move about on a blockchain protocol, and offer afundamental advantage. While a typical blockchain exposes the value ofthe recorded transaction, hiding only the identities of the traders, theBitMint blockchain may (or may not) hide the traders, and it can alsohide the value of the transaction. The BitMint public ledger onlyidentifies the coin id, not the coin value.

Accounting

This section contains tracking data, chain of custody, and various otherparameters, like method of transfer. BitMint coins may be blank on theirhistory, or fully detailed with their history, or anything in between.The purpose of this section is to be able to track down the movement ofmoney. Such functionality is important in situations where abuse, ormisuse is a question to be checked. It is also of great importance forunderstanding the behavior of a community of traders. Money flowreflects the performance and the actions of the trading environment.

This section will keep track of the change of coin status, frompre-birth (pregnancy), live and well, to dead and not buried, then deadand buried.

Chain of Custody: The sequence of owners of the coin may be secured viaa hash-signature cascade: The BitMint chain of custody is used to trackcoins as they split away among traders

BitMint Coin Cascade

The heart of a BitMint coin, [

]₀, is its payload, which in turn is an ordered set of financial bits(fbits). Each financial bit is comprised of identity bits, and databits. The value of the BitMint coin is the sum total of values of itsfinancial bits. The value of financial bit φ_(i) at position i in thepayload is defined by a respective value function (v) and the value datain the fbit (F_(dv)).

v(i)=v(φ_(i))=v(F _(dv)(i))

We now consider the case where F_(dv)(i)=w(i), where w(i) reflects adefinite monetary value and where v(i)=w(i) for i=1 to i=s. s being thenumber of fbits in the coin. The value of the coin will be:

₀ =Σv(i)=Σw(i) for i=1 to i=s

The monetary values w₁, w₂, . . . w_(s) may all be expressed as BitMintcoins: w₁=[

₁], w₂=[

₂], . . . w_(s)=[

_(s)], and hence:

₀=Σ[

] for i=1 to i=s

This construction defines a BitMint coin in terms of ingredients BitMintcoins. Each of these ingredient BitMint coins, in turn may also bedefined in terms of respective ingredient BitMint coins, and soindefinitely—a cascade.

We define a “cascade addition” of BitMint coins as:

₀=

_(12 . . . s)=[

₁]+[

₂]+ . . . [

_(s)]

The value of

₀ depends also on its coin data:

[

₀]=

₀

*

* represents the coin-data of the BitMint coin. The incorporation of

* into the summation of the fbits is the important distinction between acascade addition and a plain addition:

_(1+2+ . . ._s)=[

₁]+[

₂]+ . . . [

_(s)]

A plain addition is simply a collection of BitMint coins. A cascadeaddition incorporates the ingredient BitMint coins in another BitMintcoin framework which may include tether data. What is actually beingcascaded in the BitMint cascade is the tethering information at eachlevel. This cascading is designed to give BitMint the flexibility toexpress any complex financial statement

If no involved BitMint coin has any tether restrictions than plainaddition and cascade addition coincide, both are valued as the sum valueof their ingredients:

_(12 . . . s)=

_(1+2+ . . ._s)=[

₁]+[

₂]+ . . . [

_(s)]

The tether data in the various levels of the compound BitMint coins needto be logically resolved. Such a compound coin may be subject toconflicting tethering and surprising results. For example a BitMint coin

_(x) may be comprised of two ingredient BitMint coins

_(y) and

_(z):

_(x)=

_(yz)=[

_(y)]+[

_(z)]

Coins [

_(y)] and [

_(z)] each express 1000$ which expires December 31 of a given year.However the tether data in [

_(x)] makes this coin redeemable no earlier than January 1st the nextyear. This situation is such that [

_(x)] is worth nothing. It cannot be redeemed after December 31st, andnot before the next January 1st.

Cascade Identity The identity-value coherence of the BitMint coin isamplified in the cascade. Let's define the coin-data of a BitMint coinas

*. We express a BitMint coin as a joint payload and coin-data, andwrite:

[

]=

*

We now write:

=φ₁ φ₂, . . . φ_(s)

And express:

φ_(i)={ . . . }_(i) F _(dci) F _(dpi) F _(dvi)

where { . . . }_(i) represents the identity bits for φ_(i). F_(dci),F_(dpi), F_(dvi) represent the data values of the counters, the pointersand the value bits of fbit i. We now write as above:

φ_(i)={ . . . }_(i) F _(dci) F _(dpi)[

_(i)]

where [

_(i)] is the monetary value represented by BitMint coin

_(i)

We now write:

[

₀]=({ . . . }₁ F _(dc1) F _(dp1)[

₁])({ . . . }₂ F _(dc2) F _(dp2)[

₂]) . . . ({ . . . }_(s) F _(dcs) F _(dps)[

_(s)])

₀*

BitMint Free Trade

BitMint was designed as the closest emulation of physical cash, enjoyingits advantages, while providing digital benefits unavailable with metalcoin and paper banknotes. It can be reduced to physicality (hybrid coin)and thereby completely substitute for physical cash, but mostly it isdesigned to be stored, paid and transacted to and from networkedcomputing devices. The BitMint coin is securely recognized for what itis by the payee, and the transaction itself may be ‘done and gone’ or‘done and remembered’. Payer and payee may or may not identify eachother, and payment can span from micro payments to large internationalwire transfers. The BitMint digital coin comes with robust securityadvantages, and built in flexibility.

BitMint is more than a digital cash. It's data framework, itsrandomness-foundation makes it an ideal framework to express anyfinancial reality, any combination of cash, credit, and risk,individually and community wide.

A BitMint coin is traded by passing on the full bit string. This actcancels the ownership of the payer and confers ownership of the passedcoin to the recipient. No account is involved, no third party: thesimple act to disclosing a bit string to a recipient constitutespayment. This act raises two questions: (i) is the transferred bitstring a real carrier of monetary value? And (ii) is the payer the ownerof the string? If the answer to either one of these questions isnegative then the payment is faulty: either mistaken or fraudulent. Andhence, it is important to provide means to assure a positive answer tothese two basic BitMint payment questions. This is done through theBitMint payment integrity assurance solutions.

The BitMint free trade is practiced in several modes: Cash-EquivalentTrade, Tethered Money Trade, Credit Trade, Investment Instruments Trade

BitMint Payment Integrity Assurance Solutions

The act of BitMint payment is conducted in association with a properBitMint integrity assurance solution. We review the following solutioncategories:

Direct Payment Integrity Assurance. This option verifies the paymentper-se. We consider three sub-categories: Live BitMint Exchange orRedemption, Public Ledger, Blockchain

Coin Continuity, Payment per time, or payment per use may be carried outvia a single coin, which pushes out the fbits one by one. A payee mayverify some initial fbits, and some running fbits with some frequency,and since all these fbits emanate from the same coin, the payee willtrust that the unchecked bits are bona fide.

Payer Credibility Assurance: This option is based on the payerpresenting good credentials to the payee to gain his or her trust, andaccept the payment as valid, without real-time BitMint verification.There are two sub-categories:

cryptographic certificate: The payer presents to the payee a certificatethat proves that the payee is a trader in good standing. The certificateneeds to be issued by a trusted authority.

prosecutable identification: The payer submits identification parametersthat would allow the authorities to track him or her down in case thepayment was a counterfeit. Biological stamps would fit this requirement.A BitMint coin may be passed along carrying with it the biological‘stamps’ of all its custodians. Relaxing the need to real-time verify apayment is helpful to both parties, and hence the payee would be willingto take some risk.

Insurance: The insurance industry is expected to offer policies wherebyaccepting a payment from a payer who shows an insurance tag will shiftthe risk of a bad payment to the insurance company.

Physical Coin Assurance: Encapsulating the payment string in a physicalcapsule with proven virginity. The capsule being in tact will convincethe payee that the money inside is valid for redemption. Such physicalcoin (hybrid coins) will be well disposed to physical cracking, whichwill expose a small flash drive or other memory device that carries thepayment bits from where they are uploaded online for cyber trade.

Direct Payment Integrity Assurance

This option verifies the payment per-se. We consider threesub-categories: [1] Live BitMint Exchange or Redemption, [2] publicledger, [3] blockchain. These sub-categories are distinguished by theactive party.

The live BitMint authentication is often considered old-fashioned but itis the fastest; blockchain is often hyped as the most trusted. Thepayer's written public-ledger is often the fittest. Blockchains may beimplemented either via adopting a standard blockchain protocol, likeEthereum, or by implementing a BitMint blockchain where the recordedtransactions identify the coin, not its value, and where the affirmingnodes are incentivized by BitMint.

Live BitMint Exchange or Redemption: This is the basic integrityassurance method. A payee received a BitMint coin from a payer, andimmediately sends it to BitMint requesting its authentication. BitMintOK signal covers both counterfeiting and double-spending issues. Withtoday's communication levels the idea of authenticating every payment,large or small, 24/7, from anywhere in the world, is not far fetched.The large payment card companies exercising this feat routinely. Thismission will be even easier for BitMint because of a new technology thatdelegates the authentication power to as many as desired paymentauthentication centers (PAC). It is important to emphasize that directmint authentication is basic in the sense that it does not require thepayer and the payee to identify themselves to each other. It is justlike physical cash which can be exchanged between two completestrangers. Of course, applicable protocols may prevent payment betweenstrangers.

The BitMint Mint The Payer & Payee The Community of Traders [1] BitMint[2] Public Ledger [3] Blockchain

BitMint direct authentication may be exercised via a network of paymentauthentication centers (PAC). It is based on BitMint mistrustful datadelegation protocol. Accordingly, a BitMint coin authentication centercan delegate the coin authentication database to a subordinate center insuch a format that will prevent the subordinate center from defraudingthe parent center. The BitMint mistrustful data delegation protocol canbe applied iteratively and generate a hierarchy of PACs. The communityof traders will be dynamically divided among the PACs, so that eachtrader will have a default PAC to service him. However, if the defaultPAC is clogged or otherwise unavailable, then a substitute PAC will takeover, using a “delayed authentication protocol”.

{[

]} denotes the primary BitMint mint. {[/

]} denotes PACs derived from the main mint, and {[//

]} denotes a next generation PAC. The aggregate information of thebuyers of BitMint coins can lead a smart allocation strategy,anticipating from where will come the request for exchange, verificationor redemption. This strategy will lead to a hierarchical allocationwhere the mint ({[

]}) will copy some of the coin data to subordinate paymentauthentication centers (PAC), ({[/

]}). And they in turn will allocate part of their coins data tosubordinate PACs ({[//

]}). The leaves-PAC will take the heavy authentication load. If they arebusy or otherwise a request for authentication is taken by a higher upPAC, that PAC will issue first a tentative authentication if the coinlooks OK on its database. The authenticating PAC will wait a shortinterval of time (milliseconds) for status updates to flow from thecorresponding leaf PAC. If the update does not regard the queried coin,then the tentative authentication is affirmed. This applies to anyparent, grandparent, etc. of the applicable leaf-PAC. See below:

BitMint mistrustful data delegation protocol: The coin authenticationdatabase CAD may be processed into a conjugate form, CAD*, such thatwith CAD* it is possible to authenticate a redemption of a BitMint coin,but it does not allow one to redeem any coin from the higher PAC,holding the original CAD. By removing this detrimental vulnerability,delegation of authentication is possible. The conjugation process may bereapplied, to generate CAD**, which allows one to Ok redemption, whilenot allowing it to use CAD** to redeem a coin with the CAD* holder. Thisallows for authentication delegation to expand into a hierarchy ofindefinite depth.

Cash Equivalent Trade

The objective before us is enabling free payment flow (trade) amongmembers of the public. Payment flow is a social language that allowsmembers of the public to express their wishes, their desires, theirconcerns, and most importantly allows them to cooperate to build theirsociety. The role of BitMint is to enable such a life-giving flow.BitMint does it by building money into daily devices, and enabling moneyflow through the channels of cyberspace. When people make a decision topay a sum to a payee, they should be able to make it without friction,without delay, without fear of fraud, or complications. And if peoplewish to keep a record, be served with a receipt, be able to prove thepayment, and be able to track and record the payment in the future, thenthey should be able to do so. BitMint was designed for this mission.BitMint accomplishes this enabling task by establishing a mint that isleaning on a supporting bank, and projecting to the trading public.BitMint Cash Equivalent Trade is exercised among three players: TheSupporting Bank, The BitMint Mint, The Trading Public. We discuss aheadthe trade dynamics, and the role of three players.

Free Trade Dynamics

The BitMint free trade dynamics is presented in various aspects. We showbelow the basic configuration. All is rested on the bank. The moneyitself, $ cash never leaves the bank. It simply moves between accountsin the bank. The bank supports the mint, which is marked in thefollowing symbol: {[

]}, or {[<0 $ 1]}. The BitMint mint interacts with the bank and per eachof its coins it interacts with a coin buyer, T_(b) and a coin redeemer,T_(r).

The BitMint trade involves a cash-like transfer between traders withoutdeposit action with the mint or with the bank. This “chain trading” iscarried out in several modes, as seen below.

Chain Trading

Traders who pass a BitMint coin to one another without depositing moneywith the bank or the mint will practice one of the various trustarrangement, or a combination thereto. This, so called “chain trading”is a critical feature in the quest to digitally emulate cash trading.Coins and banknotes are ‘chain traded’ outside the perimeter of thebank, generally with complete anonymity. Only the trader to whom thebank issued the coins or the banknotes, or the trader to whom the bankredeemed the coins or banknotes will be known to the bank. This‘anonymity trading’ is often abused by a criminal element. When emulatedwith a BitMint digital coin, the beneficial aspects of chain tradingwill be preserved, but the abuse will be well countered. Some chaintrading configurations are presented below:

Zero-Trust Trading: This is the case when the payee does not trust thepayer, and does not trust the payment. The payee will then send the paidBitMint coin to the BitMint mint. If the payment is authenticated by themint then the mint will void this coin, and send down to the inquiringtrader a different coin of same value and same terms (tether). Seebelow: Payment-Trust Trading: Here the payee accepts the payment becausehe or she trusts the payment. This trust may be based (i) on a physicalcapsule in which the coin is embedded. Or (ii) based on advancedchemistry and material science where reading the coin destroys it.Another (iii) option is based on a “pay-as-you-go” draining coin, whichwas previously authenticated. Payer-Trust Trading: This tradingprocedure is based on payer's credentials. The payee accepts the paymenton account of the payer providing proof for being a BitMint trader ingood standing. Public-Ledger Trading In this trading solution the payeewill consult a public ledger that will list the BitMint coin which ispaid to him as currently being under the legal possession of the claimedpayer. Upon payment the payer will update the public ledger to reflectthe change of ownership. Insurance Based Trading In this setting thepayee will buy insurance against faulty payments. The insurer will setsome conditions, for example, checking that the payer is on the insurer‘trusted list’. The insurer will assume some of the trading risk.Blockchain Based Trade The trade with BitMint coins will be exercisedthrough any robust blockchain protocol, but with a fundamentaladvantage: The respective public ledger may hide or disclose theidentity of the trading (in bitcoin these identities remain hidden), andalso will hide or disclose the amount of money traded (in bitcoin thismount remains exposed).

The BitMint Mint

The BitMint mint, {[

]}, is the heart of the BitMint system and operation. It is comprised ofthree parts:

The BitMint Negotiator, {[

]N}

This module communicates with the three essential partners to theBitMint operation:

-   -   The Bank, {¥}    -   The Coin Buyer, T_(b)    -   The Coin Redeemer, T_(r)

It collects money from the Buyer, credits money to the Redeemer, andshifts funds among the three pertaining bank accounts: the Mint account,the buyer's account, the redeemer's account.

The BitMint Core, {[

]C} The BitMint core is accepting minting requests and responds withminted BitMint coins.

The BitMint Coin Repository, {[

]R} This module keeps track of minted coins—their status and history. Wewrite:

{[

]}={[

]N}+{[

]C}+{[

]R}

The Supporting Bank

The BitMint operation hinges on a supporting bank. While the BitMintmint manufactures the digital coins, disseminates them and redeems them,the mint is not holding the money that is passed through it, and itrequires a bona fide bank to lean on. The supporting bank will take norisk, and assume no additional responsibility on account of supportingthe BitMint operation, except as to its commitment to make all the fundsof the BitMint deposit account available in full without delay (howeverunlikely this scenario). On the other hand, the greater the activity ofBitMint, the more deposits are made available to the bank with all thebenefits thereto. From the point of view of the bank the BitMintoperation is a revenue source. Its attraction brings in money from otherbanks to the supporting bank. As BitMint grows, so does its depositaccount with the bank—more cash on hand. While the bank will have tocommit to making the entire deposited sum available upon request—that isa fundamental premise of the BitMint operation—the bank runs its ownrisk and stress tests, and may take into account the likelihood of asudden demand on funds.

Closed System: The protocol may first be limited to traders who haveaccounts with the supporting bank. In that case there is no change inthe total amount of deposits as the BitMint operation rolls ahead. Fundswill simply be shifted around between accounts in the bank, and much ofit will linger in the BitMint coin deposit account. The nominal sequenceof actions in the closed system BitMint process is: (i) money iswithdrawn from a bank customer's account to the BitMint deposit account,where it lingers as long as the respective BitMint coin trades among themembers of the public. Then (ii) when the coin is finally redeemed, themoney is shifted from the BitMint deposit account to a bank customeraccount.

Open System: The BitMint coins are sold like any merchandise so thebuyers may be any members of the public, not just banks' customers. Whenthis happens then the supporting bank benefits from influx of deposits,and the greater the BitMint activity, the larger is the net influx ofmoney to the bank. Conversely, non-bank customers when they redeem aBitMint coin will direct the money outside the bank, so the bankbenefitted only during the coin trading time. Alas, there are severalsubtle ways to influence such external traders to open an account withthe supporting bank. A local account will mean that the redemption moneyis immediately available, without a delay. Same frictionless benefitwhen that customer wishes to buy another BitMint coin. Some inducementmay be offered to the redeemers. It is clear that the BitMint activitycreates a strategic attraction towards the supporting bank, and it is apowerful engine of growth.

The Trading Public

Physical cash, inherently, is tradable without a trace. BitMint digitalcash technology offers a perfect match, however, unlike regular cashwhere the mint is powerless against abuse and misdirection of itsproducts, the BitMint mint can issue any desired level of control tobuild a track record of where the money traversed, and to limit its flowin any imaginable way. In other words, the BitMint cash equivalent tradeoffers the benefit of physical cash without its inherent shortcomings.We define three categories of traders:

Bank Customers. These are traders who have accounts with the supportingbank and are well known entities.

Traders Who Bank in Other Banks. These are fully documented traders thatmay be lured by the supporting bank.

Undocumented Traders: Traders who are not buyers and are not redeemers,but in-between holders of a BitMint coin—like cash. BitMint technologycan eliminate this class of traders, if so desired.

Limiting BitMint Trade to Bona Fide Registered Traders: This restrictioncan be exercised by a ‘chain of custody’ protocol. Accordingly theBitMint coin will carry with it the record of its chain of owners. Thischain will have to identify only registered owners, otherwise the coinwill not be redeemed.

Business Model

The BitMint initiative is a source to several revenue channels, some ofthem direct, some indirect.

Direct Revenue Channels:

Coin Purchase Fee: A coin buyer will pay a small percentage fee (e.g.0.2%)

Coin Redemption Fee: A coin redeemer will pay a small percentage fee(e.g. 0.3%)

Exchange & Verification Fee: Charging a small (but recurrent) fee forexchanging, or verifying a coin (e.g. 0.01%)

Float: The BitMint deposits held with the bank are counting as the bankreserve and participating in the bank revenue generation program. If thebank and the mint are separate financial entities then the bank will payinterest to the mint.

Residual Revenue: Digital cash may be marked with an expiration date. Ifthe mint continues to operate beyond that date, then a new digital coincan be issued, otherwise regular funds will be used. This is importantin order to allow a mint to close for business, if so desired, and it isa very potent anti money-laundering tool. There will be a residue ofcoins not redeemed by the expiration date, yet another source of revenuefor the mint.

Indirect Revenue Channels: The boost in positive image, publicity andreputation will readily translate to greater business penetration. Whena similar BitMint payment system is installed in a different location,even a different country, then this BitMint operation will be welldisposed to facilitate long-range and even international payment throughBitMint to BitMint collaboration. The broadened scope will open a newrevenue channel for the bank. Collaboration between two BitMint mintswill allow a Chinese merchant to sell his merchandise abroad, and bepaid with BitMint digital money denominated in a foreign currency. Themerchant will submit this foreign digital coin for redemption at hislocal supporting bank. The supporting bank will send this foreign cointo the foreign mint, and upon authentication of payment, will credit theChinese merchant with the Chinese currency equivalent of his coin. Ofcourse, any legal taxes, tariff, fees, etc. will be deducted from thepay. The Chinese and the foreign BitMint mints will reconcile theirstatus every day or, as frequently as desired. Such international tradewill be conducted in compliance with both countries regulations. It maybe one sided: money can flow to China, but not out of China.

Priming: Payment systems are viral in nature, and this property can bewell utilized as PayPal recently, and Visa and MasterCard earlier, havedone. Instead of pouring money into excessive advertising, it may bewiser to invest money in reverse fees. To prime the BitMint trade theoperators might offer a reverse fee to purchasers and redeemers. You buy100¥, you get 101¥, and when you redeem 100¥ you get 100.5¥, forexample. When the trade picks up, the reverse fees fade away, and arereplaced with nominal fees.

Long Term Revenue Outlook: In the long range it is anticipated that themost lucrative and powerful aspect of BitMint will be tethering. Smartcontracts, tracking, security are all clear useful benefits tocustomers, and providing them will be duly charged for. This might leadto a situation where cash-equivalent trade is free or almost free, whileprofits are generated from tethering fees.

Tethered Money Trade

Tethered Money Trade is based on cash-equivalent trade described above,adding to it restrictions for use. This is a fundamental issue. Moneygained its centrality on account of its fungibility—its universality.Tethered money is not universal money, and trading with it amounts torobbing money of its basic attraction—that it is desirable everywhere,any time, we all want more of it. Money can be tethered, restricted inany way, form, or fashion that can be reduced to a computer code. TheMajor categories for tethering are: Time of Redemption Restriction:Specifying a window of time when the money can be redeemed. Code ofRedemption Restriction: Specifying a redemption code to be submitted bythe redeemer, without which the coin will not be redeemed. RedeemerIdentity Restriction: Specifying who has the right to redeem aparticular coin Transaction Restriction: Restricting redemption based onwhat was purchased with that money. We distinguish between mint-imposedtethers and trader-imposed tethers.

Trader-Imposed Tethers: The nature of the BitMint coin makes it welldisposed to be embedded in a digital stream of conditional payment. Asimple way for trader-tether is to buy a BitMint coin tethered to aredemption code. The coin buyer will then make a payment from this cointo a merchant. The merchant will be able to clear with the mint that thecoin is authenticated and payable upon submission of the redemptioncode. The merchant will be assured that the funds to pay for itsmerchandise are available, and he will rush to fulfill his terms ofservice and supply, to satisfy the buyer, so that the buyer will releasethe redemption code.

Tethering may be cascaded. For example the mint will cascade a coin tobe restricted to purchase food, its current owner will add restrictionto buy only vegetable with that coin, A third level cascading willrestrict the coin to purchasing of tomatoes.

Mint-Imposed Tethers: The mint will be asked to impose tethers on anyunearned money, namely money that is given on some conditions, someexpectations of use. However complicated such conditions might be, aslong as they are specific enough to express in a computer program (aTuring condition) then it will be fused into the coin, and that coinwill be redeemed only when the terms are fulfilled. Complicated businesscontracts can be reduced to Mint-tethered money.

Tethered money is most consequential in business contracts where thepaid moneys are restricted by technology to what the contract dictates:

Credit Trade

The BitMint financial platform may be used to manage articles of debt,not just articles of cash. This is carried out via the negative BitMintvaluation function. More details at a later date.

Investment Instrument Trade

Modern society leverages the community to share the risk for long termexpensive undertakings. The BitMint formalism can fittingly serve thisgoal. BitMint can be structured to allow for a risk-balance long termprojects, and will allow for abstract trading of risk, as well asdigitizing any widely used commodity. An attractive way to curb risk isto digitize a piece of real estate, which people can see and developconfidence towards its lasting value.

Risk-Balance Long-Term Projects

Long term expensive projects involve a complex coordination ofactivities and their funding. The resulting contract specifies theserelationship, and is used by each party to monitor the other, spotdiversion from the contract, and then spend legal efforts to resolve anyarising conflict. Much of it can be avoided by simply translating thecontractual relationship into computer code which is tethered to thepaid BitMint funds.

The utility of the BitMint solution is that once the terms are agreedupon and written into the money, then there is no need for follow-upaccounting, payment inspection, and conflict resolution. Without BitMintthe contractor getting hold of fungible funds may use them other thanspecified by the contract. The payer will then have to expend accountingenergy to spot these changes, and then spend legal energy to resolve thearising conflict. When the money is paid in BitMint coins, it cannot bediverted outside the strict tethering specifications fused into thecoin. To the extent that the contract was faithfully encoded into themoney, there is no need to correct misspending, because misspending doesnot occur in the first place. Long terms projects experience a stressbetween the need of the project implementers to insure sufficientfunding to complete the implementation plan, and the opposite need ofthe investors to insure that their money is well used and not misused inthe fog of the project. This stress can be well handled via the BitMintplatform which satisfies the project implementers that the money isthere and would be paid to them when they reach the agreed uponmilestones. The BitMint protocol also satisfies the investors that themoney they have laid out will only be paid when and if the agreed uponmilestones have been achieved.

Abstract Trading of Risk

BitMint formalism can be used to spread long term risk. Let X and Y betwo commodities with a ρ(0)=X/Y(t=0) price ratio between them at timepoint t=0. At a future point t=t′ the price ratio would beρ′(t′)=(X/Y)_(t=t′). An entrepreneur E may approach a BitMint mint toissue ‘abstract BitMint coins’ in the form: [

X′, E, ρ′(t′)]. This will amount to an obligation by E to exchange anamount X=X′ of commodity X at a ratio ρ′ with commodity Y, at time pointt′. This abstract minted coin will be offered for sale to the public,and will trade with a moving price as time goes on. The coin will bestructured at any desired resolution, so traders can split and dividesuch a coin and trade it like cash. These abstract coins will enjoy thefull cyber protection inherent in the BitMint formalism. Theseinvestment coins may be traded on a blockchain, or through a regularpublic ledger, or they may be traded in privacy, as the case may be.

Modern industrial complexity might create a functional correlationbetween four commodities: X, Y, Z, W. This correlation might call forcascading. The coin issuing entrepreneur may wish to hedge his bet onthe expected price ratio between commodities Z and W, and cascade itsX-Y BitMint coins into a higher coin which is tethered to the ratioρ″(Z/W) to time point t=t′:

_(X,Y,Z,W)=[

X′, E, ρ′(t′)][

X′, E, ρ′(t′)] . . . [

X′, E, ρ′(t′)]

[

]=

_(X,Y,Z,W)[ρ(Z/W)≤ρ″, t=t′)]

This cascaded BitMint coin can be split and spread in the market, as thecase is with every BitMint coin. The so structured coin will limit theexposure of the issuing entrepreneur. He will have to honor his X-v.-Yobligations only if the price ratio between commodities Z and Wsatisfies the tether.

Alternatively, the entrepreneur E might operate as a publicly tradedenterprise, and might create a cascaded coin tethered to the price ifits stock at time point t=t′:

_(X,Y,Estock price)=[

X′, E, ρ′(t′)][

X′, E, ρ′(t′)] . . . [

X′, E, ρ′(t′)]

[

]=

_(X,Y,Estock price)[E _(stock price)≥{threshold}, t=t′)]

There may be many entrepreneurs E, E′,E″ fueling up the market with suchabstract BitMint coins, which are circulated in the public. Such coinsmay be countering each other. An obligation to exchange an amount X=X′of commodity X at a ratio ρ′(t)=ρ(X/Y) at time point t=t′, will becountered by a second obligation to exchange an amount Y′=Y of commodityY at same ratio ρ′(t), where X′=ρ′(t)Y′. We write:

[

: X′→Y′]+[

: Y′→X′]=0

The BitMint abstract investment coins may be publicly displayed, orsecretly traded, either way the randomness-bashed BitMint security willhold.

BitMinting Real Estate

Real estate projects project trust due to their size, immobility, andvisibility. Therefore ownership shares in such an entity are attractive,especially to people that live around the construction and reassurethemselves daily of its utility and worth. So much as digitizing fiatcurrency, BitMint can be utilized to raise money from the public toconstruct an expensive piece of real estate. To build a bridge, theenterpriser will issue ownership stakes, and promise to distributedividends from toll income. These real-estate ownership coins will befreely traded, if so desired. Alternatively these coins may limitownership to local residents, and assign voting rights to coin holders.With their votes the coin holders will decide on business practice.

For example: A community might set out to build a much-needed tollbridge across a local river. To raise money, the community issuesBitMint coins that represent stake in the bridge. These coins areimplemented with a strict chain of custody, and only local citizens canlegally purchase such coins. Every quarter the coin holders vote onproposal to adjust the crossing toll for the bridge. Since the peoplewho pay those tolls are members of the community that holds the stakesfor this bridge, the question of a fair toll will be resolved within thecommunity, giving the people a sense of control over their destiny.

Guided BitMint Trade

Every government is using money flow to exercise its responsibility.BitMint is designed to facilitate such activities. We discuss thefollowing:

Taxation: BitMint offers the efficiency of real-time taxation. Anytaxable payment, upon redemption may send the tax-due to the taxationauthority, and release the balance untethered to the redeemer.

Social Equity Payment: BitMint offers an important distinction betweenmoney earned against labor, and in trade, versus unearned money which isprovided to various segments of society in need of government help. Theformer will be untethered, and the latter will be tethered to limittheir use for the purpose for which these moneys are paid. Thisdistinction will deter abuse of the social payments. It's a practicaland psychological advantage to have untethered money that is free to beused anywhere, for any purpose.

Population Behavior: Government can steer people to certain behaviors byplanning discounts and incentives which are expressed via BitMinttethered money. Future cars loaded with digital money, might payspeeding fine, real time. The paid fines will be reported on thedashboard, thereby discouraging risky driving.

Police Work: When hunting for a hiding criminal, it might beadvantageous to impose a non-anonymous payment regimen, mandating thatevery payment, large or small, will be using BitMint coins. This willhave the identity of all payers exposed, including the identity of thefugitive.

The InterMint. It is believed that the BitMint representation of moneyis mathematically the most efficient way to combine value and identity,and as such will become popular everywhere. This implies that moreBitMint mints will blossom up in the financial meadow. We designedmint-to-mint protocols (The InterMint) to facilitate a global setupwhere interaction between mints takes the main load of long distancefinancial collaboration. The mints could be connected through nominalcommunication lines or through a blockchain configuration.

BitMint (Inclusive) Construction Scheme

We define a generic scheme for money. Money is an object of valuerecognized within a society of traders. While every object which isattractive to some degree by a sufficiently large number of traders canquality as ‘money’, we tend to distinguish money as such objects wherethe attraction for them is (i) wide spread within the community oftraders, and (ii) stable—not a whimsical attraction. These distinctionare qualitative and hence the definition of ‘money’ is quite flexible. Aquantity of money is recognized as a ‘coin’. We define a BitMint(inclusive) coin (BMIC), or “coin” as an entity of transactional valuesubject to “terms of transactions”. The terms of transactions arelogical unambiguous conditions that must be met for the coin totransactable. We use the symbol

to designate a BitMint (inclusive) coin. The value of BMIC is marked asV(

), and the terms of transactions for the coin are marked as

_(t). A coin does not need to be materialized, not even well defined asto its intrinsic properties, it just has to be uniquely labeled. ABitMint (inclusive) coin is comprised of sub-coins. The sub-coins areoptionally labeled entities configured in an “unbound geometry”, (SeePatent Application No. 62/813,281) forming a “properly evolved space”.This implies that the n sub-coins comprising a BitMint (inclusive) coinare mutually defined via a distance matrix. A distance matrix is an n×nmatrix where the sub-coins are listed both as columns and as rows, andthe cells of the matrix designate a positive integer representing the‘distance’ between the rows sub-coin and the column sub-coin. Thedistance between a sub-coin and itself is zero. As constructed thedistance matrix will be marked with the main diagonal all zeros, and theupper triangle above the main diagonal is symmetric to the bottomtriangle below the diagonal. Requiring that the space defined by thedistance matrix is ‘fully developed’ requires that no sub-coin will havethe same set of distances from all other sub-coin, as another sub-coin.This requirement insures a unique identification of each sub-coinaccording to its (n−1) distances towards the other sub-coins. A distancefrom sub-coin i to sub-coin j is the same as the distance from sub-coinj to sub-coin i. We note that each sub-coin is fully identified in thecontext of the coin by the list of its distances from all the othersub-coins. The value of the BitMint (inclusive) coin is the sum total ofthe values of the n sub-coins. We designate the n subjoins as φ₁, φ₂, .. . φ_(n):

=[φ₁, φ₂, . . . φ_(n)] and marking the value of sub-coin i as v(φ_(i)),we state: V(

)=Σv(φ_(i)) . . . for i=1,2, . . . n

A sub-coin, φ, may be a label-only type (“label-optional-coin”, LOC,φ_(LOC)), in which case its value is a function of its position in the‘space’—namely defined by its n−1 distances from all other sub-coins. Asub-coin, may also be a BitMint (inclusive) coin per se, for which avalue v(φ) is defined along with terms of transactions φ_(t). In thatcase the value of the sub-coin within the parent coin is defined interms of both the coin value of the sub-coin, per its transactionalterms, and also defined in terms of the sub-coin configuration in thespace defined by all the sub-coins. v(φ)=f(S, V(φ)) where v(φ) is thevalue of φ in the parent coin, and V(φ) is the value of φ as a φ coin. Sis the space defined by the 0.5n(n−1) mutual distances between the nsub-coins. A sub-coin which is itself a BitMint (inclusive) coin, mayagain be comprised by its sub-coins. This is an iterative process, whichends with a sub-coin that is not another BitMint (inclusive) coin. It israther a string of qbits—whether real or simulated. A sub-coin in theform of a string of q qbits will have a value defined by its distancesfrom all the other (n−1) sub-coins despite the fact that as qbits, theirbit identities is not resolved. This is a fundamental feature of theBitMint (inclusive) coin. In a simulated qbit situation, the value ofthe string sub-coin will also not be dependent on the bit identities ofthe string, despite the fact that just prior to minting of the coin theidentities of those bits was established. We use the term ‘financialbit’ fbit to designate the sub-coins of each coin. The value of BitMint(inclusive) coin will be the sum total of the values of its financialbits. Each fbit may be comprised of sub-fbit, or it may be a real orsimulated qbit-string. Note that each coin in the hierarchy isassociated with its own term of transactions. This coin hierarchy wasdesigned to encompass the digital expression of anything financial:cash, credit, debt, and all financial instruments of any purpose. Theuse of the ‘unbound geometry’ space in the construction of the BitMint(inclusive) coin aimed to allow for a sufficiently rich configuration offbits. For most practical purposes the general ‘unbound space’ maycollapse to an ordered list, where each fbit will be fully identified byits position in the ordered list. In an ordered list an fbit isidentified by its position in the string (no label needed). Similarly inthe more general case where the n fbits mutually identify themselvesthrough their 05n(n−1) mutual distances. The valuation function willspecify value to an fbit identified by its (n−1) distances from theother fbits.

The Boundary Control Principle

The design of the BitMint (inclusive) coin is motivated by the “BoundaryControl Principle” which states: “Money should be centrally minted, andultimately redeemed by the same mint, but between these boundaries ofminting and redeeming the movement, transaction, operation and use ofthe BitMint (inclusive) coins should be in the hands of the tradingpublic which the BitMint (inclusive) system is designed to serve.”

This implies sensitivity towards privacy, expressed via flexibility asto how much transactional history needs to be recorded in the coinmetadata, and it refers to the issue of trust and security. Anyone can“mint” a string of bits. It is a challenge to assure the payee that thebits coming his way are worth their purported value. The principle meansof the BitMint (inclusive) coin methodology is to rely on high qualityrandomness. It is expressed through the identity-only bits within thefinancial bits, and it may be additionally expressed via the randomizeddistance matrix that configures the fbits of a coin in a ‘space’—a setof mutual distances designed to complement the randomized bits withinthe fbit with randomized data of the relative configuration of thosefbits within the coin. Proper handling of the fbits distance matrix willprovide a trail for the mint, or to any investigator to realize thedynamics of the coins as they progressed from minting to redemption.

The fbit Space

As described the fbits within a coin are mutually configured in a‘space’ defined via a distance matrix that specifies 0.5n(n−1) distancevalues among the n fbits within a coin. This ‘space’, these distances,mutually identify the fbits in terms of each other, and specifies arelationship. There are ways to let these distances reflect somesituation among the fbits, like the example of risk-affinity. Oralternatively, these distances can be used to overlay a layer ofsecurity and accountability to the coin. Enabling thereby more freedomfor the trader to handle the coins.

If the 0.5n(n−1) distances between the n fbits are all randomized when atrader passes to another an fbit, φ along the (n−1) distances betweenthat fbit and the other fbits in the paid-from coin, the payer thenfurther proves that he or she are in possession of the claimed coins.φ_(i)(d_(i,1), d_(i,2), . . . d_(i,n−1)) where d_(ij) is the distancebetween φ_(i) to φ_(j). Each coin may be defined with its ownrandomization space, namely the range of integers from a low, l, and ahigh h integer such that every distance, r, in the coin will be arandomized selection ,within this interval: l≤r≤h. If an fbit istransferred from a previously split coin then it will reach its nextpayee with fewer distances. The number of distances itself isindicative. To redeem the coin split (the fbits) it will be required toidentify the distances submitted with the fbit by its payer, and themint will be able verify these values to insure bona fide status.

We may define the notion of ‘fbit centrality’, Ω, as the sum of itsdistances from all other fbits: Ω(φ_(i))=Σd_(ij) . . . for j=1,2, . . .n

If the selection of distances is such that no two fbits have the same Ωvalue, then this value becomes an fbit-identifier. This implies thatfbits may be addressed, referred to, and transferred without an explicitid. Their Ω value becomes their de-facto id.

BitMint (Inclusive) Coin Dynamics

Money was designated above as an entity of wide spread stable attractionthroughout the community of traders—the society of reference. TheBitMint (inclusive) idea is that this ‘money entity’ should bemanufactured with designed attributes to make it easy, safe, andefficient to trade with. This manufactured money entity should bede-materialized, an information-package. It should have no attractionper se, only attraction by agreement. The reason is that any entity ofan attraction per se is treated unevenly by the community of traders,some like it more, some like it less. An abstract entity,attractive-by-agreement can be universal. And being abstract it is easyto handle, store, and transact. It is also easy to mint, and easy toredeem. The BitMint (inclusive) coin structure as described above isconsidered an optimized flexible solution to meet this challenge. We nowdefine the dynamics of the BitMint (inclusive) coin. Since the BitMint(inclusive) coin is not a natural entity, it must bemanufactured—minted. To that end the community of traders, the societymust erect a “mint”. The mint (BitMint) will issue BitMint (inclusive)coins and redeem them. Between minting and redemption the coins aretransacted within the community of traders. We discuss ahead thedynamics of minting/redemption, and trade within the community oftraders.

Minting/Redemption

The BitMint (inclusive) coin mint will use good randomness source tobuild the payload bits of the fbits—the identity carriers. it will keepa strong back up system and a front database to work with to handleredemption of coins as they come back to be redeemed. All the coins withall their fbits will remain logged in the mint, to allow for any levelof back accounting necessary.

Trade within the Community of Traders

Traders can pass to each other an entire BitMint (inclusive) coin.Traders can split BitMint (inclusive) coins and join BitMint (inclusive)coin. When a BitMint (inclusive) is split, each split acquires the fullmeasure of the transactional terms of the original coin. If coin Csplits to C₁ and C₂, then we write: T(C)=T(C₁)=T(C₂) Where T(x) meansthe ‘transactional terms of coin x’. When two coins are joints the termsof their respective transactions are joint. Using the above notation, wemay write: T(C)=T(C₁)∪T(C₂)

Trading within the community will require some added data to the metadata of the BitMint (inclusive) coin so that the mint will be able totrace the splitting and the joining that happened to the originallyminted coin. This is necessary for proper redemption of the coins,

Coin Splitting

A coin

comprised of n fbits: φ₁, φ₂, . . . φ_(n) defined with mutual distances[i,j] between φ_(i) and φ_(j), for ij,=1,2, . . . n may be split in2^(n) ways. Every subset of m fbits may be separated to one coin split,C₁ leaving the other n-m fbits as the other split, C₂, such that:V(C)=V(C₁)+V(C₂) Where C is the pre-split coin, and V(X) is the value ofcoin X.

The split may happen in two modes: ‘fbit-split’, or ‘f-split’, and‘valuation-split’ or ‘v-split’. In an f-split each coin carries only theinformation regarding its own fbits. In a v-split each coin retainsinformation of all the fbits in the original coin, only the valuationfunction is adjusted. In an f-split the split coin carries the fbitswith its distances. So the m<n fbits in the split are defined with0.5m(m−1) distances, and all the 0.5n(n−1) in the original coin. Theminimum split size is 2 fbits defined through their mutual distance.Since the fbits are defined through the distance matrix between them, asplit with a single fbit has no distances, and is not well defined. Forthe f-split to be well defined all the 0.5n(n−1) distances of theoriginal coin must be distinct. E.g.: 1,2, . . . 0.5n(n−1) so that eachsplit will be fully identified. We may write: V(C)=Σv(φ_(i)) . . . fori=1,2, . . . n V(C₁)=Σv(φ_(i)) . . . for i=1,2, . . . m, V(C₂)=Σv(φ_(i)). . . for i=m+1, m+2, . . . n

In a ‘v-split’ all the fbits are carried in every split. The valuationfunction is the one spitted. In the simplest case split 1 retains thevaluation of m fbits, assigning the valuation of the remaining (n−m)fbits to zero, while the other split retains the valuation of the (n−m)fbits, and assigns to zero the valuation of the m fbits of the split.Clearly the sum values of the splits is the value of the pre-split coin.We may write: V(C)=Σv(φ_(i)) . . . for i=1,2, . . . n V(C₁)=Σv₁(φ_(i)) .. . for i=1,2, . . . n, V(C₂)=Σv₂(φ_(i)) . . . for i=1,2, . . . n wherev(φ_(i))=v₁(φ_(i))+v₂(φ_(i)) . . . for i=1,2, . . . n

v-splitting is of special interest in the case where the valuationfunction of an fbits is comprised of several complementary valuationfunctions. Let v be the valuation function of a given fbit. Let v becomprised of v₁ and v₂, such that v(φ)=v₁(φ)+v₂(φ). The coin where thisfbit is fitted may be split to one coin where the valuation will bev₁(φ) and another where the valuation function will be v₂(φ). It is ofspecial interest when v₁ is positive valuation and v₂ is of negativevaluation (debt).

Coin Joining

Coin C_(m) comprised of m fbits, and coin C_(n) comprised of n fbits maybe joined to form coin C_(p) where p=m+n, and where:V(C_(p))=V(C_(m))+V(C_(n)) and: T(C_(p))=R(C_(m))∪T(C_(n)) By assigningnm distances so that each fbit has assigned distances to all the fbitsof the opposite coin. We mark |X| as the number of fbits in coin x, andwrite: |C_(m)|=0.5m(m−1), |C_(n)|=0.5n(n−1) and:|C_(p)|=0.5p(p−1)=|C_(m)|+|C_(n)|+mn

The added mk distances may be of same value if the coins and theirsplits are handled in the v-split mode. If they are in the f-split modethen all the distances must be unique, and the joint coin will have0.5p(p−1) unique distances, or a bit less. It will be less because thereis no need to establish a distance value to an fbit for which thevaluation function is zero. The joint coin will have to carry meta datathat would reveal to the mint, when it comes to redemption, how thejoint coin was joined, so that the mint can properly redeem the jointcoin.

qbit—Real and Simulation

At some point in the future we will have the technology to maintaincoherence over time and keep qbits in their “virgin” form. Such qbitswill be minted as labels of fbits.

And will be transacted in coherence. The qbit will be resolved uponredemption. Until then we simulate this situation by (i) using a quantumrandomness source to determine the bit identities of fbits just—and notbefore—the BitMint coin is minted. Transaction of a BitMint coin amountsto transfer of fbit bit identities to the payee. Knowledge of the bitidentity of the fbit is proof positive of being paid, or ownership ofthe coin over anyone for whom the record shows that the same knowledgewas acquired earlier.

In other words payment of a BitMint coin is instantaneous, there is no‘dead time’ like with checks and other payments.

Meaningful fbit Distances

As described the distance values among the fbits are arbitrary and of nospecial meaning. This can be upgraded to assign meaning to the fbitdistances. We discuss here risk-linkage fbit distances. As constructedthe fbits that comprise a BitMint (inclusive) coin are defined via thedistance matrix, and may in turn be BitMint (inclusive) coin themselves.Each such sub-BitMint (inclusive) coin may be defined over a differentunderlying commodity. One may be denominated in gold, the other insilver, and the third in oil, while the rest in US$. If two such fbitsare judged as tightly linked in terms of valuation risk, then they wouldbe marked in the coin through a small distance. If they are judged to beremotely linked then the distance assigning between them will be large.

Taxation

Taxation is procedurally easy, fair, transparent and resistant to fraud.It is essentially based on the notion of coin splitting. Any amount ormeasure of BitMint (inclusive) coin may be split to a portion that is by“societal force” assigned to society-at-large aims, and the other splitthat is left under the control of who owned the pre-split coin. This waytaxation may happen without the mint having the chase the owner of aparticular coin. The splitting is done at the mint with public exposure.So the coin owner and the trading public all know that the pre-taxedcoin is now worth less because it was taxed. And the new value is publicinformation, even if the ownership of the coin may not be. Taxationsplitting may be in the form of an f-split, or a v-split. It may beacross the board, so that every coin in the space is equally taxed, orit may be graded, some coins based on any number of conditions are taxedmore than others. The mint could assign randomness to pick coins atrandom for the purpose of taxation.

Review of the Notion of Financial Bits

A BitMint (inclusive) coin is a collection of financial bits bound by astamp of meta data, and terms of redemption. The financial bit is thevalue carrying entity, and it is designed with great flexibility inorder to serve the varied complexity of modern finance. Similarly, therelationship between the financial bits (fbits) of a given coin is setup with maximum flexible construction, taken from the notion of ‘unboundgeometry”. The combined purpose is trust, versatility, efficiency andsecurity. The configuration of fbits within a coin may range frommaximum flexibility expressed by arbitrary distance values for thein-between fbit distances, to the simple idea of an ordered list whereeach fbit has a specified location on that list. The implementer of anyBitMint (inclusive) coin system will choose the right form of fbitconfiguration.

The configuration of fbits within a coin may be designed to remove theneed to assign a label, an id, to each fbit. If the fbit is in positioni on an ordered list 1,2, . . . i,(i+1),(i+2) then this position definesthe fbit without equivocation. If the full ‘unbound geometry’ space isimplemented then as long as the centrality metric of each fbit isunique, each fbit is fully identified. The centrality metric is simplythe sum of all the (n−1) distances from an fbit to the other (n−1) fbitsin the coin. The actual integer values of the distances may be set toreflect some affinity among the fbits, or it may set to boost thesecurity of the system owing to the randomized selection of distancevalues.

As to the fbit itself, it may range from a simple one bit, or a stringof t bits—all ‘payload,’ namely bits such that their identity has noimplication as to their monetary value; up to a template that includespayload and fbit meta data for various purposes, including for thepurpose of serving as an input parameter for the fbit valuationfunction. Here too, the implementer of a particular BitMint (inclusive)system will choose the right fbit design.

Valuation Function—Elaboration

BitMint money (basic mode) is comprised of a string of bits such thatthe identities of the bits carry no information about the value of thestring. This leaves the bit-count as the sole bearer of value, as theidentities of all the bits are used for establishing a unique identityto the monetary value of the string. This bit-count to value mapping iscarried out via the BitMint valuation function (V=V_(BitMint)). Countingthe bits of a given BitMint money string S from left to right, i=1,2, .. . |S|, the value of the first i bits will be V(i), denominated in thecurrency digitized by the BitMint digital money. The value contributionof the bit in the i position, v(i) is: v(i)=V(i)−V(i−1). And hence:V(i)=Σv(j) for j=1 to j=i. The BitMint valuation function V is definedover i=1 to i=|S|, and is not defined over V(t) for t<1 nor for t>|S|.In the general case the v(i) may be positive, zero, or negative, asinterpreted ahead: The most common, “natural” case is: v(i)>0 for i=1,2,. . . s, where s is the bit count of S: s=|S|. This implies that the bitis position i represents a valuation expressed in the digitized currencyexpressed in the string S. When a transmitting trader passes bit i to arecipient trader, it is construed that the transmitter paid therecipient v(i) amount of the digitized currency. For security reasonsthe minimum number of transmitted bits that would qualify as a ‘payment’may be preset number quite larger than one, but nonetheless each bit inthe money string is associated with a monetary value identified by theBitMint valuation function. The case where v(i)=0, is one where thisparticular bit does not represent any value, and transmitting it fromone trader to the other does not manifest a process of cash payment (notransfer of the digitized currency or commodity). The case where v(i)<0is one where the bit in position s carries a negative monetary value.This implies that the transmitter in that case is imposing on therecipient a monetary obligation in the amount of v(i). By accepting thisBitMint money string, the recipient acknowledges this obligation. TheBitMint coin includes meta data that may specify the terms of thisobligation, mainly with respect to time of honoring this obligation. Theuse and the implications of these three valuation options will bediscussed below.

The BitMint payment process is comprised of communicating a substringT∈S from a transmitter to a recipient. T is comprised of t=|T|consecutive bits in S. The transmitted Value, V_(t)=Σv(i) for i=t_(b) toi=t_(e), where t_(b) is the position of the first, the beginning bit ofT in S, and t_(e) is the position in S of the ending bit of T. Also:V_(t)=V(t_(e))−V(t_(b)−1). Since v(s) may be positive, zero or negative,so is the range of options for the value of the payment transmission, T.

The Positive Valuation Case

This is the case where v(i)>0 for i=1,2, . . . |S|. In this case thetransmission of any bit represents a positive payment, namely a transferof monetary value from the transmitter to the recipient.

In the most common case v(i)=v(j)=β for i,j=1,2, . . . |S|. And in thatcase the transmission of a substring T∈S constitutes a payment ofV_(t)=β*|T|. The holder of a BitMint string S, wishing to make a paymentof V_(t) can do so by sending |S|−|T| strings of size |T|. These will beequivalent payments. The T string may start with the first bit of s:i=1, or at i=2,3, . . . etch up to i=|S|−|T|. The 2nd case is theaccelerated case where v(i)>v(i−1), and in that case a substring T thatis positioned further to the right on S will represent a higher monetaryvalue than a string T′ of same length (|T|=|T′|) positioned furtherleft. This allows a transmitter to choose between high and low values,or to choose what will be the exact size of a payment string that willdeliver a known monetary value. Accelerated BitMint money strings mayhave distinct geometry: early steep, or late steep categories. An “earlysteep” string will have large v(i) values for bits closer to thebeginning of the string, and low v(i) values for strings closer to theend of S. It's the opposite for “late steep” strings. Both categorieswill allow a transmitter to make small payments as well as medium andlarge payments using roughly the same number of transmitted bits. Thetransmitter will simply properly select the location of T on S. Thevariant bit value may be used to schedule variant payment over time,with the string size remaining constant, but the value changes fromstring to string.

The Zero Valuation Case

In its simplest manifestation this case will reflect a BitMint moneystring where the monetary value of the string is zero. This is the casewhere v(i)=0 for i=1,2, . . . |S|. In that case also V(i)=0 for i=1,2, .. . |S|. Transmitting such a string, or part thereof does not constitutea transfer of value (payment). It serves though to test a system, totransmit information, to obfuscate an observer, and to track conduct andbehavior. Zero value bits may also appear as a substring T₀ in S. Thismight be useful in several protocols. Zero value bits may be padded to avalue substring T→T∥T₀, to create any desired effect, and to preventinformation leakage. A value-less substring T₀ can also couple betweentwo transmitted value strings T₁ and T₂, connected by the value-lesssubstring T₀.

The Negative Valuation Case

When the value contribution of a bit i, v(i)<0, is negative, thentransmitting it implies imposing a payment obligation on the recipient.In practice it means that when the recipient redeems those negative bitswith the mint, the mint then credits that amount to the transmitter ofthe bits (after being paid that amount by the redeemer, or from anyother source). There are several situations when this negative monetaryvalue becomes handy. Two trading partners may operate in an environmentwhere it is easier for bits to flow one way, as opposed to the other. Inthat case, paying will be accomplished by receiving negative value bitsrather than by transmitting positively charged bits.

The negative bits may be part of an agreed discount. A transmitter pays$X to a recipient, as part of an agreement for a discount at the amountof $Y. This situation could be resolved by transmitting $(X-Y), but byso doing the record of the original price and the discount thereof isnot reflected in the transaction. By transmitting a string T_(x)μT_(y),which is the combined strings T_(x) representing $X, and a string T_(y)representing −$Y, the terms of the transaction are preserved in thehistory of the payment. In pledge situations where a donor pledges todonate a sum $X to a cause. That cause will transmit a string T_(x) ofnegatively charged bits to the donor, to preserve the pledge. It will beup to the donor to pass this string to the mint, for the mint to debitthe donor account in favor of the cause.

Loan situation: When a loan-maker loans $X to a borrower, the loantransaction may be consummated by the loan-maker passing two stringsT_(x) and T_(y) where T_(x) represents $X and T_(y) represents−$(X+R)—negatively charged. Where R represents the interest due on theloan at the time when the loan is due to be repaid. T_(x) is readilypayable. The borrower can use it to make payments, consistent with theterms of the loan (which are written into the BitMint digital coin metadata section). The T_(y), on the other hand will be payable at a laterdate, when the loan is due. The borrower then will pass the T_(y) to themint, which will then debit the borrower account and pay the loan maker(either with BitMint money or otherwise).

Full Variability BitMint Valuation Function

A BitMint coin may be a combination of the three types. The valuefunction V(s) may take any form, regardless of the total value of thecoin V(|S|). Some sections of V may be flat, others may be a straightupward line or a straight downward line, and yet other sections may beparabolic or exponential, etc.

The coin string and the valuation function may be held separately.Consider a coin-holder (CH) unaware of the valuation function, andconsider separately a valuation-function holder (VFH), who is not awareof the identities of the |S| bits of S. The VFH will be charged withmaking payments based on the valuation function, which it knows. The VFHwill then determine that the coin holder should make a payment in theform of communicating to the payee a string say, T, which is asubsection of a full BitMint coin, string S, and is comprised of thebits from position i to the bit in position j in S. The VFH will thencommunicate the details of T to the coin holder (CH) for execution. Thecoin holder, (CH), will execute the transfer of money string T definedfor it by the VFH as the substring that starts with bit i and ends withbit j. The CH may not be aware of the sum paid, much as the VFH may notbe aware of the identities of the paid bits. This separation may beutilized in various security protocols.

Superposition Valuation

A BitMint coin, B, may represent w distinct currencies C₁, C₂, . . .C_(w), each with measure c_(1b), c_(2b), . . . c_(wb). We define herecurrency as a unit of measurement and quantification of either thepossession of value or of obligation of value, namely as credit, or asdebit. This abstraction of the notion of currency allows BitMint to usethe same rails to move around both cash and credit. It's a fundamentalprocess advantage to represent both cash and credit in the same format.According to the BitMint principle the coin B should be redeemed againstwell specified amounts of these w currencies. A trader who comes toredeem, say, half of B (0.5B) will receive half of the coin quantitiesfor each currency 0.5c_(1b), 0.5c_(2b), . . . 0.5c_(wb). We first assumethat these w currencies can be added. In that case the valuationfunction V(s) can be written as the summation of the w currenciesrepresented by this coin. V(i)=ΣV_(j)(i) for j=1,2, . . . w for eachi=1,2, . . . |S|.

In the general case a simple arithmetic summation is impossible, and theset of individual currencies superposition on the digital coin is themost concise way to express the coin. In the simple case the valuationfunctions for each currency will run parallel in a mutually coordinatedway. But this is not necessary. For simplicity we analyze the case ofw=2: a BitMint coin that represents two currencies, X and Y. We firstcomment that the following discussion only makes sense for twocurrencies that are not readily interchangeable. Because if there is aready conversion coefficient α, such that y=α*x, where x and y are givenquantities of currencies X and Y respectively, then we have:

V(i)=V _(x)(i)+V _(y)(i)=V _(x) +αV _(x) =V _(x)(i)*(1+α)=V′ _(x)(i)

And the superposition issue is readily condensed into a single BitMintvaluation function. The same applies for w>2, if all the w currenciesare readily interchangeable.

We conclude then that the currencies are not readily interchangeable. Infact the currencies may be of different nature: one may be regularmoney, another may be access time to a privileged service, a third maybe an accounting device, to follow on the activities of payers andpayees. The various currencies may also be essentially the same currencybut with a different redemption date. This prevents a risk-free exchangerate, and deny the existence of a simple “α” as we have seen above. Onemay note that any superimposed BitMint coin may be exchanged to two ormore single-valued coins. The advantage in the multi-valued coin is theeconomy of the ‘smart contract’, that is the metadata that is used totether the money or the obligation to their terms. Multi-valuation alsoguarantees the connection between the various expressions of value. Theyall travel together as the coin is moved around.

Illustration: A buyer and a seller agree on terms. Accordingly, thebuyer can buy up to some 500 units of merchandise for a total of$100,000. $80,000 of which are payable in cash, and the balance, $20,000payable at a specified later date. Using BitMint, the cash will beregarded as the X currency, and the delayed payment regarded as a Ycurrency (recall the abstracted interpretation of currency above). Inthe simple case, the mint would issue a money string S comprised of,say, |S|=2,400,000 bits. Accordingly we will have:V_(x)(i)=(80,000/2,400,000)*i=(1/30)*i, for i=1,2, . . . 2,400,000. AndV_(y)=(20,000/2,400,000)*i=(1/120)*i for the same range of i.

The buyer may argue that the merchandise will not fit very well, so hemay buy only a small amount, and in that case he may wish to pay less.However, if all fits the buyer will agree to pay the full sum. This canbe accomplished using a “late steep” valuation function, of the formV_(y)(i)=β*i². It is easy to find the value of β, since if the entireagreed amount is actually purchased, the buyer will pay the full amount:Y=$20,000. Hence V_(y)(i=2,400,000)=β*i². This computes to:β=(20,000)/(2,400,000)²=0.347*10⁻⁸.

For comparison let's see how much does the buyer pay after ordering 250units of the merchandise. The payment for this amount will be a stringof BitMint money of length: (250/500)*(2,400,000)=1,200,000 bits,transferred from the buyer to the seller.

First the linear case: The seller will submit the 1,200,000 bits to themint and in return will have an immediate credit in its account of the Xcurrency, valued as V_(x)(i=1,200,000)=(1/30)*(1,200,000)=$40,000. Themint will also send the seller new BitMint money at the value of the Ycurrency: V_(y)(i=1,200,000)=(1/120)*(1,200,000)=$10,000. This BitMintmoney will only be redeemable at the designated redemption date, andonly if the buyer account has sufficient funds at that time.

In the second case, (“late steep”) the X currency will be the same, butthe Y currency situation will be different:

V _(y)(i=1,200,000)=β*(1,200,000)²=(0.347*10⁻⁸)*(1,200,000)=$4990

Less than half than in the linear case. The mint will convey to theseller a BitMint money string in the amount of $4990 redeemable notearlier than the designated redemption date.

Of course, if all the 500 units are ordered, then the two casescoincide. The way the value is structured over the bits of the coin,together with the dynamics of passing them around, amounts to a paymentorder that reflects the agreed upon distribution of assets, risk andobligations. And to the extent that the coin and its meta data isexposed beyond the payer and the payee, this is also a means fortransparency.

In trading practice the mint may issue the full string of 2,400,000 bitsupfront to the buyer, to pay with this string to the seller. Howeverthis BitMint coin will be marked with a ‘not redemption ready’ markerthat would progressively be removed when the buyer actually pays themint for more and more bits in the string. The Y currency bits that areissued by the mint to the seller are nominally pre-paid for by thebuyer. And if not, then they come with a note that makes it clear thatit is expected that the buyer will pay the mint the Y amounts before thedue date, and this expectation is a condition for redemption. The mintitself does not take chances. This arrangement via BitMint utilizes thecredit and reputation both the seller and the buyer have with BitMint,as opposed to mutual strangeness between the seller and the buyer.

Use Cases

Some use cases discussed here:

-   -   Complexity Activity Accounting    -   Credit Management

Complexity Activity Accounting

Money per-se emerged as a very effective regulatory device. Modernsociety is comprised of thousands of different job titles, eachconsuming resources from others and delivering a valuable product to hisor her customers. This dynamics is recorded, tracked, and motivated bythe flow of money. This situation will also apply to any complex,non-hierarchal highly interactive environment as is envisioned for theInternet of Things and the Internet of Everything. If any node in suchan interactive network is charged for every service it gets from othernodes, and is getting paid for every service it delivers to other nodesthen the record of the network money flow will be a record of theactivity of the network. A record needed for accounting purposes, forliability management, and as a basis for study and research into thedynamics of the network in order to improve it. This vision makes itvaluable for networks to interact-with-pay, to pay and get paid forevery service however small. This can be done with BitMint money ofnominal value or of zero value, where there is no wealth transfer onlyaccurate accounting of the activity of the network. It is thefrictionless property of BitMint payment, defining payment in its mostbasic mathematical element: amount and identity of coin, that makes iteconomical to account for payment per the tiniest service or product,and thereby follow network dynamics, and study it in ways unavailableotherwise.

By attaching to each BitMint coin the full record of its custody chain,it becomes more and more difficult for hackers and abusers to falsifyrecord, to steal identities, and game the system. To take the role of anode in the network, the hacker will have to steal the victim's money,along with the victim's means to assert his, her or its identity.

Credit Management

BitMint manages cash and credit over the same rails, with the samespeed, security and versatility. When a transmitter sends BitMintbit-wise money to a recipient, it may be positively charged (valued),where it is a cash equivalent, or it may be negatively charged(negatively valued), where it is credit (loan, obligation). With BitMintsuperposition protocol a loan can be extended with the terms of itspay-back captured within the same money string. The loan giver willcreate a superposition. The positive charge (the cash of the loan) witha negative charge, which implies money that the recipient is to pay thetransmitter at a time specified in the metadata associated with thetransmitted coin. This superimposition will be at bit-wise resolution.The fact that the very same bits are associated with both the loan andits repayment (positive and negative BitMint valuation functions) allowsfor this BitMint money to be moved around. It enables smooth accounting,and management of a credit cascade where an original loan maker makes aloan to a first recipient, who then passes all or part of that money toa second recipient—passing the cash and the obligation to pay back, allin the same string of bits. The BitMint user has a great deal offlexibility in structuring the cash-credit superimposition. We presenttwo ways:

-   -   1. Ongoing Interest: in this way every amount of cash passes, X,        obligates the recipient to pay Y=(1+r)*X, where r represents the        interest on the loan. BitMint will issue a value string S. The        bits in S will be associated with a positive valuation function        V_(x)(i)=β*i for i=1,2, . . . |S|, and a negative valuation        function V_(y)(i)=−(1+r)β*i for i=1,2,3, . . . |S|. With every        amount paid as cash, the recipient assumes a corresponding        obligation.    -   2. Late Interest: in this way a loan in the amount of $X made at        time point t=0, is to be returned as a sum $Y>$X at time point        t=1. The BitMint money will be expressed as a money string T_(x)        marked positive with a BitMint valuation function V_(x)(i), for        i=1,2, . . . |T_(x)|, and also marked negatively by        V_(y)(i)=−V_(x)(i) for i=1,2, . . . |T_(x)|, plus another string        R, representing $R=$Y−$X, for which the positive part will be        zero V_(r)(j)=0, and the negative charge will be less than zero        V_(r)(j)<0 for j running from the first bit of R to the last bit        of R.

Cascaded Credit

A BitMint coin with double valuation of positive value (cash) andnegative values (credit, obligation), is a mechanism to capture both themoney transfer, the issuing of the loan, and the obligation to pay backthe loan at specified time with given conditions. Such a double-valuedcoin may be further divided and issued further, and then againrecursively. Each payer of the obligation will secure a receipt from itspayee, which will be the basis of any claim, if the credit is not repaidas agreed. In summary, there will a cascade of loan giving with aparallel cascade of receipts. If this cascade is exposed in an openledger then it allows others to see the credit/cash situation of thetraders.

Illustration: Let Alice issue a $1000 loan to Bob on January 1st. Themoney is issued through a double valued BitMint coin which includes thepositive valuation function V(i) per bits i=1,2, . . . |S|, where S isthe BitMint money string, and a negative valuation function V′(i), suchthat V′(|S|)=1050, due on July 1st. Bob then divides the BitMint coin totwo halves, giving one half to Carla and the other half to David. Carlaand David each receives cash in the amount of $500, with obligation topay $525 on July 1st. The coin can cascade down any number of times.Carla and David will be responsible for repayment of the loan to Bob,and Bob will be responsible for repayment to Alice.

Open Credit Ledger

Bitcoin introduced the innovation of a public ledger that details thedistribution of the bitcoin money among its traders. A similar publicledger can detail, document and make public the distribution of BitMintmoney among its traders. This includes super-imposed BitMint money, andin particular credit and cash distribution. Credit extended via BitMintmay be made public, with the traders being masked or being exposed asthe case may be. This will give the trading public a detailed view ofrisk distribution. When the traders are publicly traded companies thenthis public ledger is of great significance for investors.

Credit Cash Resolution

A set of traders will exchange cash and credit in ways that will be wellrecorded and expressed through the BitMint payment platform. Everynegative valuation of a BitMint coin may be neutralized with a positivevaluation of a matching coin. The accounting of positive and negativemoney valuation provides accounting clarity and versatility in ways thatresemble the versatility and clarity that was experienced by arithmeticwhen the natural numbers were expanded to integers.

Illustration: Alice issues a BitMint coin to Bob, for the sum of $5000,on February 1st. Bob agreed to repay the loan on November 1st of sameyear at the sum of $5250. Bob, in turn has secured a grant for itsresearch, which includes a pre-paid sum of $8000, which will be releasedfor Bob's use on October 1st. Bob can then ask the mint to reassign$5250 out of the $8000 as cash claimed by Alice and in return nullifyhis negative obligation on the coin given to him by Alice. Bob will nowhave $5000 to use without further obligation, because he used theBitMint coin accounting procedures to assign money coming to him lateras money that satisfies his contracted obligation.

In another case the $8000 to be given to Bob on Oct 1st are in a form ofcredit, promise to pay, not pre-paid. In that case Bob can also assign$5250 from that promise as credit in favor of Alice. Alice might releasethe obligation of Bob, if she considers the source of the $8000 promiseto be more reliable, but would not release Bob from his obligation ifthe source of the $8000 promise is not sufficiently reliable.

BitMint Payment for Daily Meds: At home patients may be delivered, say,once a month, a locked box including all their daily drugs for a periodof a month. The box will release the daily pills, when paid. Payment maybe accomplished using NFC communication (among other methods, likeBluetooth) where the patient's smartphone loaded with BitMint digitalmoney is sending over money bits, against which the locked box drops thedaily pills. The BitMint app on the phone will only send over bit moneythat satisfy the timing requirements written into it, and the box forits part will only accept digital money that comes with terms proper forthe release of the drugs at that moment. A monthly visit will replacethe box, or the patient will carry the locked box to exchange it with anew one. The money accumulated in the box will either be communicatedthrough the air (e.g. 4G) to a central money register, or be stored inthe box and drained from it when it is retrieved empty of pills from thepatient. The pay-per-pill drug-dispensing app will alert the patient ifthe daily pills have not been purchased. It might also alert thephysician of record. The locked box might also be on guard for anydeviation from the regimen, and respond according to a pre-programmedalgorithm.

BitMint Frictionless Payment

BitMint money system and payment protocols are hinged on the notion offrictionless payment. Money is valuable in motion, in transfer. Paymentgives money its value and its service. This act of payment must beclean, and unencumbered to the highest degree. At the same time itshould be clear, unambiguous, doubt-free, also without reservations. Toaccomplish that it is necessary to separate the act of payment from anyother concerns, especially security and fraud. Such concerns will beaccommodated around and on top of the basic frictionless act of payment.BitMint payment is believed to be the ultimate simplicity in actualizingthe act of payment where a coin of any desired value is passed frompayer to payee. When the payee gets possession of the coin the act ofpayment has been completed. The term ‘coin’ is used here to highlightthe fact that payment in its essence is a transfer of anidentity-specific item of a specific value, from payer to payee. Thesetwo parameters are essential for the act of payment to be happening. Thenotion of a coin reflects this combination. A coin is a distinct item,distinguished from all other coins of same or different denomination,and an item that is clearly marked as to the value to it represents.BitMint is the ultimate mathematical simplicity of making a payment.When a BitMint bit string is communicated from payer to payee, thetransaction is done.

The BitMint bit-wise coin payment is a strict analog to passing aphysical coin. When a payer hands over a physical coin to the payee,there is no intrinsic need for mutual identification. Two completestrangers may exchange money. Alas, all the prevailing paymentmechanisms involve intrinsically an identification of both payer andpayee, either explicitly or implicitly. That is because these areaccount-based payments. The payment amount is identified via anidentity-less figure; so to make the payment stick, the identity of thepayer and the payee must be established. This is the source of frictionfor legacy transactions as well as the common cryptocurrencytransactions. BitMint is free of it, and that is why it can be donefrictionless, which, in turn, is why the BitMint payment will work formicro and nano payments, however fast they need to happen. BitMintpayment is in the form of passing some bits. Upon their passing thepayment occurs even if the identities of the payer and payee have notbeen established.

Because of this utter simplicity of transferring an identity unique,value-specified coin from one to another, it behooves on us to applythis solution to the transfer of anything of any value from one toanother. So the term currency used in BitMint descriptions should beextended. The extension applies first to items of values that arereadily exchanged with each other at some established exchange rate,(say a dollar v. Yuan, or Euro v. Gold), then extended to items ofvalues that are not readily interchanged, like dollar, andaccess-privileges, or stock v. priority status for a medical procedure,like an organ transfer, etc. Next the term currency may be extended toitems of very transient value, like discounts, ephemeral coupons.Currencies may also be taken in a negative notion of obligation, andhence the BitMint machinery can be used to manage credit and risk. Oncethe payment per se has been stripped to bare bones, one has to mind theissue of trust and security. With BitMint such issues will be dressedupon the essential payment. The trust and security for BitMint paymenthas four categories:

-   -   Zero Trust Verification    -   Side Trust Fund    -   Behavioral Trust Index    -   Insurance

Elaborated on below:

Zero Trust Verification: when two mutually mistrustful strangersexercise a payment, the payee will not consider the payment done untilshe cleared the paid money with BitMint, and likely have been given afreshly minted money string in the same amount (replacing the presentedstring). This works like credit card payments today. The payment isverified by the network, who then assumes responsibility for the paymentamount. BitMint zero trust verification has a fundamental advantage oversimilar verification for other payment systems. The BitMint systemallows for delegation of verification authority, so that a transactionmay be verified by a near-by local verification center.

Side Trust Fund. This solution calls for all the traders to deposit withthe mint a reservoir sum, Z, which is significantly larger than themaximum transactional threshold H (Z>H). These reservoirs will allow thetraders to transact within this closed environment without verifyingeach transaction with BitMint. Instead every payee will insist onreceiving a cryptographically robust identification data for theidentity of the payer. Every so often each trader will convey theaccumulating money paid to BitMint for verification. If any payment doesnot pass the verification, then the trading license to the apparentlyfraudulent trader will be revoked and the defrauded trader will be paidfrom the reservoir of the fraudster. The timing for the aggregatereporting has to be adjusted to prevent a trader from launching amassive fraud with many traders before he is caught. One may recall thatto pay with counterfeit money is considered a serious felony, which isan effective deterrent especially for smaller sums.

Behavioral Trust Index: traders develop a history of behavior with themint. As they do so, the mint will issue to them a trust index thatincreases in value the longer the trader has well behaved both timewise, and transaction volume wise. It takes a while to build a trustindex. Each trader will be able to present his trust index in acryptographic form that would assuage the payee that no fraud isinvolved (e.g. using public/private key technology). The payee maydecide that for a high enough trust index, and a low enough sum ofpayment, the risk of accepting the payment without real timeverification from BitMint is well worth it. Anyone abusing the trustindex will lose it right away, and may be denied another index for life,or for a long time. The convenience of payment without waiting forverification will be prized by all traders, and they would not opt tolose it. Merchants might let payers without a trust index wait in adifferent line, and impose other inconveniences.

Insurance: this payment trust challenge gives rise to a classicalinsurance opportunity. Merchants and other payees may buy insurance thatwould say that if the payee accepted payment of sum Z from a payer thathas presented a trust index of I, and it was eventually found out to bea fraud then the insurance will compensate the payee. This shifts therisk from each payee to the insurance company. Insurers will be able tooffer their own trust indices to traders, and then insure traders whoaccept payment from a payer with an insurance issued index. The field isrich with opportunity. The important point here is that the question ofpayment fraud is not impacting the payment solution itself which is keptat its mathematical minimum, and lends itself to building upon it richvalue transfers configurations.

EXPLANATION OF DRAWINGS

FIG. 1: BitMint Valuation Function This figure illustrates eightdifferent functions. Each function is depicted on a graph where thehorizontal axis marks the ordered bits of a string S comprised of s=|S|bits listed from left to right, and the vertical line represents themonetary value identified for various substrings of S, V(i) for i=1,2, .. . s Each point on the graph, V(i) with horizontal value i and verticalvalue V(i), reflects the value of a substring of S defined as theordered bits from bit one to bit i. The value of a substring thatstretches from bit i to but j is given by V(j)−V(i−1). The figuredepicts the following cases:

Case (a) is the simple function where each bit in the BitMint bit stringcontributes the same monetary value, and hence the value of a string isproportional to the number of bits it contains. The respective valuationfunction is a straight upward line starting at the origin. The greaterthe slope, the greater the value contribution of each bit. A string T oft bits somewhere in the stretch of |S| bits of the coin string S will beof same value regardless of which t-size segment of S is being markedfor T. Case (b) depicts an “early steep” function where the first bits(counting left to right) value high, up to a point i where the valuetapers off. A fixed size string T marked at the beginning area of S willhave a larger value than a same size string T marked further to theright of S. This allows one to adjust string size to payment sum. Smallpayments may be cut out from the right area of S where each bit isvalued less and large payments may be cut out from the left area of Swhere each bit is valued more. Case (c): This is the opposite of case(b), the left side bits have a smaller value and the bits near the endof the string have an increasingly higher value. Case (d): this is thezero value case, where the bits carry no value, and their transferconstitutes a zero payment. The value of such a payment is foraccounting, activity tracking and testing a real payment system. Case(e) This case is a combination of cases (b) (c), and (d) where theBitMint valuation function changes in per bit valuation from high valueto lower value to zero value, and then it rises again, low level thenhigh level (steep curve). Case (f): this case introduces the negativebit concept. A bit associated with a negative value represents amonetary obligation rather than a monetary asset. The absolute value ofthe bit valuation function reflects the measure of the obligationassociated with the bit. The picture shows a coin S where the first bitsthereof represent value, and the latter bits represent obligation suchthat the total value of the S string, the coin, is zero. Obligation likeassets may be untethered or may be tethered. An untethered obligation isa due obligation, a tethered obligation may be effective at some laterdate, or contingent upon some future event. Passing a coin like (f) is azero payment transaction because the assets and the obligations cancelout. The owner of such a coin could make regular payments by passing onsubstrings of S from the left side of S where the bits carry a positivevaluation, or she could be paid by passing on bits from the obligationzone of S. This would amount to passing the obligation to another party,presumably in some fair trade where the coin owner transfers somethingof value to the party that agrees to assume the obligation entailed inthe right side of S. Case (g): This coin depicts a negatively valuedBitMint coin, namely a statement of obligation. The holder of this coinis associated with an obligation to pay. The payment may or may not betethered to any terms of repayment. In the depicted case each bit in Scontributes the same measure to the coin's obligation. Hence the holdercould pass along any substring T∈S, from any section of S, and the valuewould be the same. This case is the symmetric opposite of case (a). Onereflects cash and the other liability. Case (h): This case depicts ageneral valuation function with positive parts and negative parts all inone coin.

FIG. 2: BitMint Payment Configuration Valuation Function Holder and CoinHolder: This figure depicts the separation option between the entitythat holds the coin, the “coin holder” (CH) and the entity that holdsthe valuation function, the “Valuation Function Holder” (VFH). Paymentcan be exercised such that the CH is not aware of the valuation of thecoin under consideration, while the VFH is not aware of identity, or thebit pattern of the coin. Together they accomplish the payment. Thefigure shows a payment request of $X coming from a prospective payee.The request is handled by the VFH who decides on fulfilling the paymentrequest by identifying a substring T of the coin string S. The VFHdefines T by its initial bit, bit i, and its terminal bit, bit j. Theidentities of i and j are then communicated from the VFH to the CH. TheCH, for its part may be clueless as to the value of S or the value ofthe payment substring T. CH only knows the values of i and j, and itcuts the T substring from i to j, erases it from its possession or marksit as paid, and delivers the actual string to the requesting payee. Thetransaction is thereby complete. The figure also shows the valuationfunction held by the VFH and how T is defined over it.

FIG. 3: Mutual Service: BitMint Payment Accounting This figure depicts asituation where a large number of interrelated items provide and consumeservices and products from each other. The items may be players in aregular human economy, or they can be computing devices in a largecommunication network. Such an environment may act in apparent chaos andunpredictability, some services are in high demand and short supply,other are in low demand and large supply. There is a great deal ofinefficiency in such a system, and therefore there is a great need to(i) study it, and (ii) regulate it. Both objectives may be fulfilledwith the help of a payment system where every service is paid for.Payment may be carried out with low value coins, or even zero levelcoins, where the objective is not the transfer of wealth and assets butto monitor the dynamics within the network. However, in order toregulate the system there must be a good pricing strategy that wouldincentivize the generations of desired, in demand, products or services,and reduce bottlenecks. Dynamic pricing, will do that. Normal naturalregulation of supply and demand will optimize the system and will serveas the justification for this payment regimen. One may note that themonitored and/or regulated payment dynamics may be comprised of assetsand liabilities, cash and obligations. The history of the paymentreality within such a network may be captured by the increasing sizetrail that follows the BitMint digital coin. In the depiction, item ornode A makes a BitMint payment (a) to node B—in a form of a bit string.At some point of time later B makes a b payment to C, where b is part ofthe a payment made by A to B. C at some point cuts the coin b andconveys part thereof, c, to node D which then passes a part or whole ofit to E. The figure shows how the coin held by E which is part of theoriginal coin a sent from A to B, is being trailed by meta data thatidentifies the full fledged chain of custody. Who owned that segment ofthe coin at which time interval.

FIG. 4: Superposition of BitMint Valuation Functions This figure shows aBitMint coin associated with several valuation functions in a “parallel”format, namely for each valuation function the relationship betweenvaluation of a bit to its previous bit is the same. On the left side thethree valuation functions shown are ‘simple’ in the sense that each bithas the same value as the previous one. But different valuationfunctions have different values. These distinct valuation functions mayindicate interchangeable commodities, or non-interchangeablecommodities, in which case this arrangement makes more sense. The rightside of the figure shows “late steep” valuation functions in parallelform. Each valuation function follows a similar pattern, but they havedifferent valuation values for each bit.

FIG. 5: BitMint Coin Superpositioned with Positive and Negative ValuesThis figure depicts the concept of double valuation of the bits of aBitMint coin. Each bit i has a positive value v(i), and a cumulativevalue V(i)=Σv(j) for j=1,2, . . . i. But it also is associated with anegative valuation function which signifies obligation: v′(i) and asimilar cumulative negative valuation function V′(i)=Σv′(j) for j=2,3, .. . i. The figure shows both V(i) from i=1 to i=s, line (a), and thenegative valuation function V′(i) from i=1 to i=s, line (b). The figurealso shows line −(a), which is the mirror image of line (a). The gapbetween this mirror line (−(a)), and line (b) reflects the edge of theobligation value over the asset value. This is a typical situation for aloan. V(i) reflects the value of the loan expressed by the size of thesubstring 1 - - - i, and V′(i) reflects the value of the correspondingobligation, typically the amount of the loan plus some interest. Themeta data of the coin will identify the terms under which the V′(i)obligation has to be satisfied.

FIG. 6: BitMint coin superposition with a Positive, Zero and NegativeValues This figure shows positive, negative and zero value bits within asingle BitMint coin. It reflects a loan situation where the owner canmake payments from this coin by cutting off substrings where theobligation matches the cash, while keeping the extra obligation burdento himself. Line (a) represents the BitMint simple positive valuationfunction. The valuation at point A reflects the full positive valuationof the coin, as expressed with the substring T of the coin S: |T|=|OB|.This substring carries assets and obligation in equal amount. It is soindicated by having the obligation valuation line shown as the mirrorimage of the positive valuation function. −(a) is the mirror of (a). Orsay |OC| is the mirror image of |OA|. The remaining part of the coin,shown as section |BE| has no positive valuation, only negativevaluation. It reflects the interest on the loan, which comes withrepayment terms identified within the coin meta data. That interest isdepicted as the vertical gap between points C and D. The section |BE|looks flat from a positive valuation view.

FIG. 7: Credit and Cash Cascade This figure shows cash and creditcascading. The top of the figure shows trader A and her coin, which iscomprised of positive valuation of $x, and a negative valuation(obligation) of $y, like in a typical loan. That coin is represented bya bit string S comprised of s bits. A could then divide her coin in someway and pass each part to a different trader. The figure shows an equaldivision. The first (leftmost) s/2 bits are paid to trader B, and thesecond (rightmost) s/2 bits are paid to trader C. Since both thepositive and the negative valuation functions are linear (each bit isworth the same as all others, both for positive and for negativeevaluation), such division equally divides both the assets and theobligation. At this point both trader B and trader C have in theirdisposal a coin which is a cut from A's coin. This implies that tradersB and C, now each owes to A $0.5y payable according to the termsspecified in the coin. A still has its obligation towards whomever gaveher the coin in the first place. In other words, A has cascaded down theobligation, passed it on to other traders. Same with the asset. Thefigure further shows how trader C divides its coin to two parts, passingeach part to another trader: the asset and the obligation. Traders D andE each now holds a coin that carries $0.25x each and carries anobligation in the sum of $0.25y. D, or E or both can continue thiscascading further. Note that when A split the coin S, it passed theleftmost 0.5s bits to B and the rightmost 0.5s bits to C. These bitscarry both the positive and the negative valuation function. When traderC passed part of its coin to traders D and E, then D got the thirdquarter of the coin S (counting left to write) and E receive the 4thquarter of the same coin.

In practice any “parent node” in this cascade might impose a mark-up ofthe obligation, which would garner some profit to this node. Otherwisethe entire paid obligation will be passed upwards.

FIG. 8: Coin Exchange: Double Valuation to Single Valuation This figuredepicts how a coin with double valuation: asset plus obligation isexchanged to two coins with single valuation each: One with a positivevaluation and one with a negative valuation. Coin A reflects cash in theamount $X>0 and liability in the amount $Y<0. The trader may exchangecoin A for two coins B and C where coin B is single valued for theamount $X, and coin C is single-valued for the obligation $Y. Coin B canbe spent, paid, right away to any other traders, while coin C comes dueat time point t as specified in the meta data of the coin. Subject tothis obligation, coin C may be traded within the community of traders.

FIG. 9: Positive and Negative Valuation Exchange This figure depicts theprocess of swapping credit with cash. It shows trader A in possession oftwo coins. One coin is double valued: $X>0 cash, and $Y<0 liability(obligation). The other coin is a cash coin with $Y tethered to a usedate. The money cannot be paid, or used before time point t. Time pointt is also the due date for the negative valuation of $Y of the firstcoin. The cash in the first coin is available immediately. The traderwho owns these two coins may exchange them as follows. Let B be thetrader who claims the $Y liability that is indicated in the coin held byA. A would exchange through the mint its double-valuation coin with asingle valuation coin for $X, this cash is available immediately, plus anew coin, that is also single valued as positive cash in the amount of$Y, only that that coin is passed on to trader B. Trader A swapped thecash coin in its possession against wiping out its negative valuation ofthe first coin. Trader B loses the hold on trader A for the $Yobligation indicated in the coin, and in return trader B now holdspositive cash which is available for use at point t. This swapintroduced no change in the holding and liabilities of either trader. Itsimply swaps risk, and generates convenience, and of course a record iskept of what had been done.

FIG. 10: Drug Authentication: The picture depicts pills spilling out ofa prescription bottle where a patient's phone takes a picture of them.The pills are marked with a unique entropic message (see appendix) andthe app on the phone compares the entropic message on the pills to whatis expected from the genuine manufacturer, to ascertain that the drugsare authentic. Critical for online orders.

FIG. 11: Nurse Verifies Patient's Pills (and pays for them) viaPatient's phone: The picture shows the tray the nurse prepared for ahospitalized patient. It also shows her taking the patient's hospitalphone to read the entropic message on the pills (see appendix),verifying that there is no error, and then pressing a payment button topay for the two pills to be consumed at the moment. The payment isthrough BitMint tethered money that can only be used for these two pillsat this particular time. If that money is not spent it indicates thatthe patient has not taken her medicine.

FIG. 12 Patient pays for daily pills and gets them: This figures shows amedicine lock box that releases the pills needed to be consumed at thismoment by a patient taking the pills at home. The pills are releasedonly after the patient pays for them. The payment is tethered to thetime these pills are to be taken. That digital money is not transactablebefore or after. See appendix.

FIG. 13: Pay-per-Pill helps Patients take their Prescription drugs ontime: This figure shows three digital coins

1,

2,

3, stored in the patient's phone. The figure also shows that at timepoints X, Y and Z the patient is scheduled to take a pill. At timeinterval a-b (some time before time point X and some time after), coin

1, is eligible for redemption (payment). It cannot be used at any timebefore point a or at any time after point b. The phone also storesdigital coin

2, which can be used only between time point c and time point d (aroundthe scheduled time for the 2^(nd) pill, Y). The figure then shows

3, which is ‘live’ and usable between time point e and f only—around thescheduled time for the third pill, Z. The phone stores these tetheredcoins for all the scheduled pills. If a coin is not used properly thephone reports to the health care center, and alerts the patient. Thisper-pill-payment helps secure the administration of prescription drugs,and helps with the accounting burden. See appendix.

FIG. 14: Patient Pays per Pill, Nurses Save Work, Reduces Errors: Thisfigure depicts a nurse approaching a hospitalized patient with her cart.The cart identifies the patient via her phone or smart device thatcannot be moved from the bed, to prevent errors. Once the patient isidentified, the computer on the cart identifies the pills needed at thattime, and connects to the patient smart device to get paid for thesepills. Once the pills are paid for, they are dispensed from adepartment-wide dispenser that houses all the prescription drugs neededby all patients in the department. The nurse saves the work of preparinga tray for each patient, several times a day. This reduces errors. Sincepay-per-pill is activated there are no subsequent bills or invoices, noargument about the veracity of the invoice. And of course the record ofthe digital payment allows for future examination of proper dispensationof the prescribe drugs.

FIG. 15: qbit—real and simulated: The figures shows the differencebetween the full qbit mode and the simulated qbit mode where the bitidentity is resolved upon minting.

FIG. 16: Splitting a BitMint Coin: The figure shows how a coin isdivided to three parts when a middle sub-string is identified along withthe previous and subsequent strings.

FIG. 17: Anatomy of an fbit: the figure shows a coin comprised of fbitsdivided to identity bits, counter bits, pointer bits and value bits.

FIG. 18: BitMint coin structure: the figure shows the data elements ofthe BitMint coin.

FIG. 19: BitMint Redemption Dynamics: figure shows how the various dataelements in the coin contribute to the coin redemption decision.

FIG. 20: owner identification options: the figure shows how the coinmetadata carried biological information of its owner to build security.

FIG. 21: coin custodian history: figures shows how the coin metadatacarries the ownership history of the coin.

FIG. 22: BitMint network Nodes confirm BitMint Transactions: figureshows the coin trajectory from minting to redemption where the ownershipexchange is confirmed by other traders.

FIG. 23: layered security for coin history: the figure shows howsuccessive records of coin history are linked cryptographically to builda trusted record.

FIG. 24: Tracking BitMint Split Coins: the figure shows how the coinattributes migrate to all the splits of a coin.

FIG. 25: frictionless payment: the figure shows how BitMint money payscontinuously from one chip (payer) to another (payee), utilizing thevery form of BitMint money.

FIG. 26: time dynamics of coin authentication: figures the relationshipbetween a tentative confirmation to a firm confirmation.

FIG. 27: Coin conjugate database stops delegation fraud: the figureshows how the BitMint hierarchy delegates authority downward, and howpayment confirmation climbs up through the same hierarchy.

FIG. 28: dynamic comparison between cash and BitMint coins: the figureshows how BitMint coin changes many hands, relative to some nationalcurrency (e.g. Chinese Yuan) that backs it up, that stays at the mint'saccount throughout the transaction.

FIG. 29: f-split of BitMint coin. The figure shows how a coin identifiedthrough an fbit distance matrix is split into two subcoins each holdsmutual distances for the fbits claimed by it. Dark circles representfbits, the lines between them represent distance values. White circlesrepresent fbits with a zero valuation function. The figure shows thatwith v-split all the fbit information is carried by both splits,including all the distance values, only that the sum valuation of thefbits in the two splits equals the valuation of that fbit in thepre-split coin.

FIG. 30 joining of BitMint coins: the figure shows how coins are joined,whereby new distance values are created to connect all the fbits to eachothers. When the joining involves coins which were previously v-splitthen the fbits with zero valuation need not be distance-connected to theother fbits.

SUMMARY NOTES

This invention presents a primary method for minting digital coins as adigital expression representing a collection of well-ordered financialbits, (fbits), viewed as claim checks for a public commodity which is inthe form of a fiat currency, gold, or silver, or any other tradableentity; the minted coin digital expression includes meta-data thatspecified the attributes of the mint, time of minting,identification-label of the coin, and the meta data further specifiesthe conditions that must be met for the coin to be redeemed (‘terms ofredemption’); each fbit may be comprised of data reflecting attributes,and it does include a number of bits, regarded as the ‘fbit payload’,such that the identity of the payload bits does not express anyinformation regarding the value of the fbit; it only defines theidentity of the fbit, for which the probability of guessing is 1/2^(n),for the n bits of the payload, as these identities are selected ad-hocby a source of high-quality randomness; each fbit is assigned avaluation function specified in the coin meta data and defines the valueof the fbit; the value of the coin is the sum values of the coin'sfbits.

The primary method is further defined wherein a coin may be split to twosub-coins, where the fbits in the pre-split coin are divided between thetwo splits; the terms of redemptions are inherited by the two splitcoins, the value of each split coin is the sum valuations of its fbits.

The primary method is further defined wherein a coin may be split to twosub-coins where the valuation function for each fbit, v(fbit), isdivided to one valuation function v₁(fbit) that is associated with thefirst split of the coin (split-1) and another valuation functionv₂(fbit) that is associated with the second split of the coin, such thatv(fbit)=v₁(fbit)+v₂(fbit) for every fbit in the coins; the valuationfunctions for each fbit for each split are written into the meta data ofeach split; the terms of redemptions are inherited by the two splitcoins. The primary method is further defined wherein the fbits aremutually defined through a set of distinct 0.5n(n−1) positive integersindicating distance values between the n fbits of a coin, such that thefbits are not in any pre-set sequence, but each fbit can be specifiedvia the set of its distances to all other (n−1) fbits; the distancevalues are written in the meta data of the coin.

The primary method is further defined wherein two coins C₁, and C₂,comprising n₁ fbits and n₂ bits respectively can be joined to a jointcoin C_(j), the value of which is the added values of C₁ and C₂, byadding n₁*n₂ distances between each of n₁ fbits to each of the n₂ fbits,and by logically creating a union of the terms of redemptions for C₁ andC₂

The primary method is further defined wherein the fbits have noattributes data, and are comprised only of n payload bits each, theidentity of which is randomly selected by the mint and does not reflectvalue of the fbits only identity of the fbits; such fbits areconcatenated to a composite string, and identified by their location inthe composite string. The primary method is still further definedwherein the fbits in the coins have a negative valuation, and in orderto redeem these coins, their holder has to pay their denominated valueto the mint; or the holder may pass such negative coin to another traderand pay, or give a value equivalent, to that other trader, which is thenresponsible for the coin redemption; such negative coins may have aredemption date, and serve to manage debt.

The primary method is further defined wherein the financial bits areassociated with a valuation function which is dependent on specifiedfuture eventualities written in the coin meta data, and in this formsuch coin can be used as an investment, and risk allocation instrument.

This invention also identifies a system for minting, transacting andredeeming digital coins whereby a central authority issues digital claimchecks against which a definite measure of a publicly traded commodityis given to the submitter of the claim check; the system allows forthese coins to be traded within a trading community; said coins areassigned with terms of redemptions specified as meta data part of thedigital coin, allowing a coin owner who satisfied the terms ofredemptions to redeem it, namely claim its denominated value from themint; and where the coins are comprised of financial bits (fbits); eachfbit comprised of meta data and value ‘payload bits’, which are bits forwhich the identity has been determined by a randomness source, and forwhich the identity of the bits does not specify any monetary value;monetary value is determined by a valuation function specified in themeta data; and where the mint keeps a database of all minted coins,indicating status of each coin as fully redeemed, partially redeemed, ornot yet redeemed; where partial redemption may be redemption of some notall the fbits, or redemption of part of the value indicated by thevaluation function of the partially redeemed fbit.

Glossary: This document describes money in the BitMint format, for whichthe registered trademark is:

. When the digitized currency is ¥ we write

(¥), and similarly

($), and

(

), etc. The trademark will also be represented with standard symbols:

=<01>=<|1> and when representing ¥:

(¥)=<0¥1> and similarly

($)=<0 $ 1>, and

(

)=<0

1>. A BitMint coin is comprised of the BitMint money bits (value bits),regarded as ‘the payload’ and of meta-data, or coin-data, marked as

* or <0|1>*. A BitMint coin will be marked as: [

]=

*=<0|1><0|1>* The value bits, the ‘payload’ is a string of ‘financialbits’:

=φ₁φ₂ . . . φ_(s) where φ_(i) is financial bit at position i in themoney string. i=1,2, . . . s, where s is the number of financial bitsthat comprise the BitMint coin.

Each financial bit is associated with a value function v_(i)=v(φ_(i)),and the coin as a whole has a value: V(

)=Σv(φ_(i)) for i=1 to I=s In the simplest implementation of BitMint afinancial bit is a nominal bit. The entity that manufactures, mints, theBitMint digital coin is called The Mint. Symbol: The BitMint Mint: {[

]}, or {[<0|1>]}. The modules inside the Mint: the Negotiator (N), theCore (C), and the Coin Repository (R) are expressed as {[

]N}, {[

]C}, {[

]R}, respectively. This symbols are used in special coin mintinglanguage developed within the BitMint program.

A BitMint Mint serves as a payment authentication center, PAC, using itscoin authentication data (CAD). CAD can be modified into CAD* such thatthe mint can delegate coin authentication function to it to authenticateBitMint payment. Such a delegated entity, (derived entity) will bedesignated as {[/

]}, and if it delegates this authority further, the newly derived entitywill be marked as {[//

]}, and so on.

What is claimed is:
 1. A method for minting digital coins as a digitalexpression representing a collection of well-ordered financial bits,(fbits), viewed as claim checks for a public commodity which is in theform of a fiat currency, gold, or silver, or any other tradable entity;the minted coin digital expression includes meta-data that specifies theattributes of the mint, time of minting, identification-label of thecoin, and the meta data further specifies the conditions that must bemet for the coin to be redeemed (‘terms of redemption’); each fbit maybe comprised of data reflecting attributes, and it does include a numberof bits, regarded as the ‘fbit payload’, such that the identity of thepayload bits does not express any information regarding the value of thefbit; it only defines the identity of the fbit, for which theprobability of guessing is 1/2^(n), for the n bits of the payload, asthese identities are selected ad-hoc by a source of high-qualityrandomness; each fbit is assigned a valuation function specified in thecoin meta data and defines the value of the fbit; the value of the coinis the sum values of the coin's fbits.
 2. The method of claim 1 whereina coin may be split to two sub-coins, where the fbits in the pre-splitcoin are divided between the two splits; the terms of redemptions areinherited by the two split coins, the value of each split coin is thesum valuations of its fbits.
 3. The method of claim 1 wherein a coin maybe split to two sub-coins where the valuation function for each fbit,v(fbit), is divided to one valuation function v₁(fbit) that isassociated with the first split of the coin (split-1), and anothervaluation function v₂(fbit) that is associated with the second split ofthe coin, such that v(fbit)=v₁(fbit)+v₂(fbit) for every fbit in thecoins; the valuation functions for each fbit for each split are writteninto the meta data of each split; the terms of redemptions are inheritedby the two split coins.
 4. The method of claim 1 wherein the fbitsmutually defined through a set of distinct 0.5n(n−1) positive integersindicating distance values between the n fbits of a coin, such that thefbits are not in any pre-set sequence, but each fbit can be specifiedvia the set of its distances to all other (n−1) fbits; the distancevalues are written in the meta data of the coin.
 5. The method of claim1 wherein two coins C₁, and C₂, comprising n₁ fbits and n₂ bitsrespectively can be joined to a joint coin C_(j), the value of which isthe added values of C₁ and C₂, by adding n₁*n₂ distances between each ofn₁ fbits to each of the n₂ fbits, and by logically creating a union ofthe terms of redemptions for C₁ and C₂
 6. The method of claim 1 whereinthe fbits have no attributes data, and are comprised only of n payloadbits each, the identity of which is randomly selected by the mint anddoes not reflect value of the fbits only identity of the fbits; suchfbits are concatenated to a composite string, and identified by theirlocation in the composite string.
 7. The method of claim 1 wherein thefbits in the coins have a negative valuation, and in order to redeemthese coins, their holder has to pay their denominated value to themint; or the holder may pass such negative coin to another trader andpay, or give a value equivalent, to that other trader, which is thenresponsible for the coin redemption; such negative coins may have aredemption date, and serve to manage debt.
 8. The method of claim 1wherein the financial bits are associated with a valuation functionwhich is dependent on specified future eventualities written in the coinmeta data, and in this form such coin can be used as an investment, andrisk allocation instrument.
 9. A system for minting, transacting andredeeming digital coins whereby a central authority issues digital claimchecks against which a definite measure of a publicly traded commodityis given to the submitter of the claim check; the system allows forthese coins to be traded within a trading community; said coins areassigned with terms of redemptions specified as meta data part of thedigital coin, allowing a coin owner who satisfied the terms ofredemptions to redeem it, namely claim its denominated value from themint; and where the coins are comprised of financial bits (fbits); eachfbit comprised of meta data and value ‘payload bits’, which are bits forwhich the identity has been determined by a randomness source, and forwhich the identity of the bits does not specify any monetary value;monetary value is determined by a valuation function specified in themeta data; and where the mint keeps a database of all minted coins,indicating status of each coin as fully redeemed, partially redeemed, ornot yet redeemed; where partial redemption may be redemption of some,not all the fbits, or redemption of part of the value indicated by thevaluation function of the partially redeemed fbit.